Maths-

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Question

1.2.3+2.3.4+3.4.5+........n terms. Find sum to n terms.

$\frac{n (n + 1) (n + 2) (3 n + 5)}{2}$
$\frac{n (n + 1) (n + 2) (n + 3)}{4}$
2n(n + 1)(n + 2)
$\frac{n (n + 1) (n + 2) (3 n + 1)}{12}$

hint Hint:

General Term ( $T subscript r space right parenthesis equals space$ $r left parenthesis r space plus 1 right parenthesis left parenthesis r plus 2 right parenthesis space equals r left parenthesis r squared space plus space 3 r space plus 2 right parenthesis space equals r to the power of 3 space end exponent plus space 3 r squared space plus space 2 r$

The correct answer is: $fraction numerator n left parenthesis n plus 1 right parenthesis left parenthesis n plus 2 right parenthesis left parenthesis n plus 3 right parenthesis over denominator 4 end fraction$

$T subscript n space end subscript equals space open square brackets n to the power of t h end exponent space t e r m space o f space 1.2.3 close square brackets open square brackets n to the power of t h end exponent space t e r m space o f space 2.3.4 close square brackets open square brackets n to the power of t h end exponent space t e r m space o f space 3.4.5 close square brackets W e space k n o w space t h a t space a subscript n space end subscript equals space a space plus space left parenthesis n minus 1 right parenthesis d T subscript n space space end subscript equals space open square brackets 1 space plus open parentheses n minus 1 close parentheses 1 close square brackets open square brackets 2 space plus open parentheses n minus 1 close parentheses 1 space close square brackets open square brackets 3 space plus open parentheses n minus 1 close parentheses 1 space close square brackets T subscript n space space end subscript equals space open square brackets 1 space plus open parentheses n minus 1 close parentheses close square brackets open square brackets 2 space plus open parentheses n minus 1 close parentheses space close square brackets open square brackets 3 space plus open parentheses n minus 1 close parentheses space close square brackets T subscript n space space end subscript equals space left square bracket left parenthesis n right parenthesis open parentheses n plus 1 close parentheses left parenthesis n plus 2 right parenthesis right square bracket W e space h a v e space t o space f i n d space o u t space S subscript n S subscript n space equals begin inline style stack sum T subscript n with blank below end style space equals space begin inline style stack sum left square bracket space left parenthesis n right parenthesis left parenthesis n plus 1 right parenthesis left parenthesis n plus 2 right parenthesis right square bracket space equals space sum for blank of left square bracket left parenthesis n right parenthesis space left parenthesis n squared space plus 3 n space plus space 2 right parenthesis right square bracket with blank below end style begin inline style stack S subscript n space equals space sum with blank below end style T subscript n begin inline style space end style begin inline style equals end style begin inline style space end style begin inline style sum for blank of end style begin inline style n cubed end style begin inline style space end style begin inline style plus end style begin inline style space end style begin inline style sum for blank of end style begin inline style 3 end style begin inline style n squared end style begin inline style space end style begin inline style plus end style begin inline style space end style begin inline style sum for blank of end style begin inline style 2 end style begin inline style n end style begin inline style blank end style begin inline style stack S subscript n space equals sum T subscript n with blank below end style begin inline style space end style begin inline style equals end style begin inline style space end style begin inline style sum for blank of end style begin inline style n cubed end style begin inline style space end style begin inline style plus end style begin inline style space end style begin inline style stack 3 sum with blank below end style begin inline style n squared end style begin inline style space end style begin inline style plus end style begin inline style space end style begin inline style stack 2 sum with blank below end style begin inline style n end style begin inline style blank end style begin inline style W end style begin inline style e end style begin inline style space end style begin inline style k end style begin inline style n end style begin inline style o end style begin inline style w end style begin inline style space end style begin inline style t end style begin inline style h end style begin inline style a end style begin inline style t end style begin inline style space end style begin inline style S subscript n end style begin inline style space end style begin inline style equals end style begin inline style space end style n over 2 begin inline style left parenthesis end style begin inline style 2 end style begin inline style a end style begin inline style space end style begin inline style plus end style begin inline style space end style begin inline style left parenthesis end style begin inline style n end style begin inline style minus end style begin inline style 1 end style begin inline style right parenthesis end style begin inline style d end style begin inline style right parenthesis end style begin inline style blank end style begin inline style S subscript n end style begin inline style space end style begin inline style equals end style begin inline style space end style begin inline style open square brackets begin display style fraction numerator n left parenthesis n plus 1 right parenthesis over denominator 2 end fraction end style close square brackets squared end style begin inline style space end style begin inline style plus end style begin inline style space end style begin inline style 3 end style begin inline style open square brackets begin display style fraction numerator n left parenthesis n plus 1 right parenthesis left parenthesis 2 n plus 1 right parenthesis over denominator 6 end fraction end style close square brackets end style begin inline style space end style begin inline style plus end style begin inline style 2 end style begin inline style open square brackets begin display style fraction numerator n left parenthesis n plus 1 right parenthesis over denominator 2 end fraction end style close square brackets end style begin inline style blank end style begin inline style S subscript n end style begin inline style space end style begin inline style equals end style begin inline style space end style begin inline style open square brackets begin display style fraction numerator n left parenthesis n plus 1 right parenthesis over denominator 2 end fraction end style close square brackets squared end style begin inline style space end style begin inline style plus end style begin inline style space end style begin inline style open square brackets begin display style fraction numerator n left parenthesis n plus 1 right parenthesis left parenthesis 2 n plus 1 right parenthesis over denominator 2 end fraction end style close square brackets end style begin inline style space end style begin inline style plus end style begin inline style open square brackets n left parenthesis n plus 1 right parenthesis close square brackets end style begin inline style blank end style begin inline style T end style begin inline style a end style begin inline style k end style begin inline style i end style begin inline style n end style begin inline style g end style begin inline style space end style begin inline style o end style begin inline style u end style begin inline style t end style begin inline style space end style begin inline style c end style begin inline style o end style begin inline style m end style begin inline style m end style begin inline style o end style begin inline style n end style begin inline style blank end style begin inline style S subscript n end style begin inline style space end style begin inline style equals end style begin inline style space end style begin inline style fraction numerator n left parenthesis n plus 1 right parenthesis over denominator 2 end fraction end style begin inline style space end style begin inline style open square brackets begin display style fraction numerator n left parenthesis n plus 1 right parenthesis over denominator 2 end fraction end style space plus space left parenthesis 2 n plus 1 right parenthesis space plus space 2 close square brackets end style begin inline style blank end style begin inline style S subscript n end style begin inline style space end style begin inline style equals end style begin inline style space end style begin inline style fraction numerator n left parenthesis n plus 1 right parenthesis over denominator 2 end fraction end style begin inline style space end style begin inline style open square brackets begin display style fraction numerator n squared space plus space n space space plus 2 left parenthesis 2 n space plus space 1 right parenthesis space plus space 2.2 over denominator 2 end fraction end style close square brackets end style begin inline style blank end style begin inline style S subscript n end style begin inline style space end style begin inline style equals end style begin inline style space end style fraction numerator n left parenthesis n plus 1 right parenthesis open square brackets n squared space plus space n space space plus 4 n space plus space 2 space plus space 4 close square brackets over denominator 4 end fraction begin inline style blank end style begin inline style S subscript n end style begin inline style space end style begin inline style equals end style begin inline style space end style begin inline style fraction numerator n left parenthesis n plus 1 right parenthesis open square brackets n squared space plus space 5 n space plus space 6 close square brackets over denominator 4 end fraction end style begin inline style blank end style begin inline style F end style begin inline style a end style begin inline style c end style begin inline style t end style begin inline style o end style begin inline style r end style begin inline style i end style begin inline style z end style begin inline style i end style begin inline style n end style begin inline style g end style begin inline style space end style begin inline style b end style begin inline style y end style begin inline style space end style begin inline style s end style begin inline style p end style begin inline style l end style begin inline style i end style begin inline style t end style begin inline style t end style begin inline style i end style begin inline style n end style begin inline style g end style begin inline style space end style begin inline style o end style begin inline style f end style begin inline style space end style begin inline style m end style begin inline style i end style begin inline style d end style begin inline style d end style begin inline style l end style begin inline style e end style begin inline style space end style begin inline style t end style begin inline style e end style begin inline style r end style begin inline style m end style begin inline style s end style begin inline style space end style begin inline style o end style begin inline style f end style begin inline style space end style begin inline style n squared end style begin inline style space end style begin inline style plus end style begin inline style space end style begin inline style 5 end style begin inline style n end style begin inline style space end style begin inline style plus end style begin inline style space end style begin inline style 6 end style begin inline style blank end style begin inline style S subscript n end style begin inline style space end style begin inline style equals end style begin inline style space end style begin inline style fraction numerator n left parenthesis n plus 1 right parenthesis open square brackets n squared space plus space 3 n space plus space 2 n space plus space 6 close square brackets over denominator 4 end fraction end style begin inline style blank end style begin inline style blank end style begin inline style S subscript n end style begin inline style space end style begin inline style equals end style begin inline style space end style begin inline style fraction numerator n left parenthesis n plus 1 right parenthesis open square brackets n left parenthesis n plus 3 right parenthesis space plus space 2 left parenthesis n space plus space 3 right parenthesis close square brackets over denominator 4 end fraction end style begin inline style blank end style begin inline style S subscript n end style begin inline style space end style begin inline style equals end style begin inline style space end style begin inline style fraction numerator n left parenthesis n plus 1 right parenthesis left parenthesis n plus 2 right parenthesis left parenthesis n space plus space 3 right parenthesis over denominator 4 end fraction end style begin inline style blank end style begin inline style blank end style$

Let $f colon R rightwards arrow R$ be given by $f left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesis to the power of 2 end exponent minus 1 comma x greater or equal than negative 1$ . Then the set of values of x for which $f left parenthesis x right parenthesis equals f to the power of negative 1 end exponent left parenthesis x right parenthesis$ is given by

Maths-General

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If $1 minus e to the power of fraction numerator 1 over denominator x end fraction minus 1 end exponent greater than 0$ , then x is not satisfied by number of integral values

Maths-General

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The domain of $f left parenthesis x right parenthesis equals fraction numerator l o g subscript 2 end subscript invisible function application left parenthesis x plus 3 right parenthesis over denominator x to the power of 2 end exponent plus 3 x plus 2 end fraction$ is

Maths-General

General

Maths-

The inverse of the function $y equals open square brackets 1 minus left parenthesis x minus 3 right parenthesis to the power of 4 end exponent close square brackets to the power of 1 divided by 7 end exponent$ is

We used rules of indices to solve the question. For such questions, we should be familiar with rules of indices.

The inverse of the function $y equals open square brackets 1 minus left parenthesis x minus 3 right parenthesis to the power of 4 end exponent close square brackets to the power of 1 divided by 7 end exponent$ is

Maths-General

We used rules of indices to solve the question. For such questions, we should be familiar with rules of indices.

General

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The domain of $f left parenthesis x right parenthesis equals square root of x to the power of 2 end exponent minus 4 vertical line x vertical line plus 3 end root$ is

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General

physics

A Shell of mass M and radius R has a point mass placed at a distance r from its center. The gravitational potential energy u(r)-v will be,

physicsGeneral

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physics

The correct graph representing the variation of total energy (E) kinetic energy and potential energy (U) of a satellite with its distance from the center of earth is.........

physicsGeneral

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physics

The curves for P.E. (U) K.E. (EEK) of two particle system ae shown in figure, At what points. system will be bound.

physicsGeneral

General

chemistry-

Which of the following structures have same configuration around the chirality centre ?

chemistry-General

General

chemistry-

The two structures given below are :

chemistry-General

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1.2.3+2.3.4+3.4.5+........n terms. Find sum to n terms.

2n(n + 1)(n + 2)

General Term (

The correct answer is:

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$\frac{n (n + 1) (n + 2) (3 n + 5)}{2}$
$\frac{n (n + 1) (n + 2) (n + 3)}{4}$
2n(n + 1)(n + 2)
$\frac{n (n + 1) (n + 2) (3 n + 1)}{12}$

The correct answer is: $fraction numerator n left parenthesis n plus 1 right parenthesis left parenthesis n plus 2 right parenthesis left parenthesis n plus 3 right parenthesis over denominator 4 end fraction$

If $1 minus e to the power of fraction numerator 1 over denominator x end fraction minus 1 end exponent greater than 0$ , then x is not satisfied by number of integral values

If $1 minus e to the power of fraction numerator 1 over denominator x end fraction minus 1 end exponent greater than 0$ , then x is not satisfied by number of integral values

The domain of $f left parenthesis x right parenthesis equals fraction numerator l o g subscript 2 end subscript invisible function application left parenthesis x plus 3 right parenthesis over denominator x to the power of 2 end exponent plus 3 x plus 2 end fraction$ is

The domain of $f left parenthesis x right parenthesis equals fraction numerator l o g subscript 2 end subscript invisible function application left parenthesis x plus 3 right parenthesis over denominator x to the power of 2 end exponent plus 3 x plus 2 end fraction$ is

The inverse of the function $y equals open square brackets 1 minus left parenthesis x minus 3 right parenthesis to the power of 4 end exponent close square brackets to the power of 1 divided by 7 end exponent$ is

The inverse of the function $y equals open square brackets 1 minus left parenthesis x minus 3 right parenthesis to the power of 4 end exponent close square brackets to the power of 1 divided by 7 end exponent$ is

The domain of $f left parenthesis x right parenthesis equals square root of x to the power of 2 end exponent minus 4 vertical line x vertical line plus 3 end root$ is

The domain of $f left parenthesis x right parenthesis equals square root of x to the power of 2 end exponent minus 4 vertical line x vertical line plus 3 end root$ is