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Maths-

General

Easy

Question

$2.1 squared plus 3.2 squared plus 4.3 squared plus midline horizontal ellipsis horizontal ellipsis plus left parenthesis n plus 1 right parenthesis n squared equals$

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

hint Hint:

In this question, we have to find the value of $2.1 squared plus 3.2 squared plus 4.3 squared plus midline horizontal ellipsis horizontal ellipsis plus left parenthesis n plus 1 right parenthesis n squared equals$ . Firstly, finding each terms equation and later finding the sum using the equations for the sum of squares and cubes.

The correct answer is: $fraction numerator n left parenthesis n plus 1 right parenthesis left parenthesis n plus 2 right parenthesis left parenthesis 3 n plus 1 right parenthesis over denominator 12 end fraction$

$a subscript n equals left parenthesis left parenthesis n plus 1 right parenthesis to the power of t h end exponent t e r m space o f 2 comma space 3 comma space 4 comma space..... comma n plus 1 right parenthesis left parenthesis n to the power of t h end exponent t e r m space o f space 1 comma space 2 comma space 3 comma space...... comma n right parenthesis space space space space equals n squared. left parenthesis n plus 1 right parenthesis space space space space space equals n cubed plus n squared n o w comma space S subscript n equals stack sum n cubed plus with k equals 1 below and n on top sum from k equals 1 to n of n squared space space space space space equals open square brackets 1 half n left parenthesis n plus 1 right parenthesis close square brackets squared plus open square brackets fraction numerator n left parenthesis n plus 1 right parenthesis left parenthesis 2 n plus 1 right parenthesis over denominator 6 end fraction close square brackets space space space space equals n left parenthesis n plus 1 right parenthesis open square brackets fraction numerator 3 n left parenthesis n plus 1 right parenthesis plus 2 left parenthesis 2 n plus 1 right parenthesis over denominator 12 end fraction close square brackets space space space space equals 1 over 12 n left parenthesis n plus 1 right parenthesis left parenthesis 3 n squared plus 3 n plus 4 n plus 2 right parenthesis space space space space equals 1 over 12 n left parenthesis n plus 1 right parenthesis left parenthesis 3 n squared plus 7 n plus 2 right parenthesis space space space space equals 1 over 12 n left parenthesis n plus 1 right parenthesis left parenthesis 3 n squared plus 6 n plus n plus 2 right parenthesis space space space equals space 1 over 12 n left parenthesis n plus 1 right parenthesis left parenthesis n plus 2 right parenthesis left parenthesis 3 n plus 1 right parenthesis$

Related Questions to study

The domain of the function $f left parenthesis x right parenthesis equals fraction numerator tan invisible function application 2 x over denominator 6 cos invisible function application x plus 2 sin invisible function application 2 x end fraction text is end text$

The domain of the function $f left parenthesis x right parenthesis equals fraction numerator tan invisible function application 2 x over denominator 6 cos invisible function application x plus 2 sin invisible function application 2 x end fraction text is end text$

Let $f colon open square brackets 1 half comma 1 close square brackets not stretchy rightwards arrow left square bracket negative 1 comma 1 right square bracket$ is given by $f left parenthesis x right parenthesis equals 4 x cubed minus 3 x text then end text f to the power of negative 1 end exponent left parenthesis x right parenthesis text is given by end text$

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If $f left parenthesis x right parenthesis equals fraction numerator 10 to the power of x minus 10 to the power of negative x end exponent over denominator 10 to the power of x plus 10 to the power of negative x end exponent end fraction text then end text f to the power of negative 1 end exponent left parenthesis x right parenthesis equals$

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If $f left parenthesis x right parenthesis equals fraction numerator e to the power of x plus e to the power of negative x end exponent over denominator 2 end fraction$ ,then the inverse function of $f left parenthesis x right parenthesis text is end text$

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If $f left parenthesis x right parenthesis equals x squared plus x comma x equals 10 comma delta x equals 0.1$ observe the following
$text l) end text delta f equals 2.11$
$text II) end text d f equals 2.1$
$text III) Relative error in end text x text is end text 1$
The true statements are

If $f left parenthesis x right parenthesis equals x squared plus x comma x equals 10 comma delta x equals 0.1$ observe the following
$text l) end text delta f equals 2.11$
$text II) end text d f equals 2.1$
$text III) Relative error in end text x text is end text 1$
The true statements are

Statement I : $f colon A not stretchy rightwards arrow B text is one - one and end text g colon B not stretchy rightwards arrow C text is a one-one function, then gof end text colon A not stretchy rightwards arrow C$ is one - one
Statement II : $text If end text f colon A not stretchy rightwards arrow B comma g colon B not stretchy rightwards arrow A$ are two functions such that $g o f equals I subscript A text and end text fog equals I subscript B comma text then end text f equals$ $g to the power of negative 1 end exponent$
Staatement III : $f left parenthesis x right parenthesis equals sec squared invisible function application x minus tan squared invisible function application x g left parenthesis x right parenthesis equals cosec squared invisible function application x minus cot squared invisible function application x comma text then end text f equals g$
Which of the above statement/s is/are true.

Statement I : $f colon A not stretchy rightwards arrow B text is one - one and end text g colon B not stretchy rightwards arrow C text is a one-one function, then gof end text colon A not stretchy rightwards arrow C$ is one - one
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Staatement III : $f left parenthesis x right parenthesis equals sec squared invisible function application x minus tan squared invisible function application x g left parenthesis x right parenthesis equals cosec squared invisible function application x minus cot squared invisible function application x comma text then end text f equals g$
Which of the above statement/s is/are true.

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