Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

If $x equals sum subscript n equals 0 end subscript superscript infinity end superscript a to the power of n end exponent comma y equals sum subscript n equals 0 end subscript superscript infinity end superscript b to the power of n end exponent comma z equals sum subscript n equals 0 end subscript superscript infinity end superscript left parenthesis a b right parenthesis to the power of n end exponent$ where a<1, b<1 then

xy+xz=yz+x
xyz=x+y+z
xy+yz=xz+y
yz+zx=xy+z

hint Hint:

We can write x as
$x space equals space fraction numerator 1 over denominator 1 minus a end fraction space rightwards double arrow a space equals space fraction numerator x minus 1 over denominator x end fraction$
Similarly, we can write y as
$y space equals space fraction numerator 1 over denominator 1 minus b end fraction space rightwards double arrow b space equals space fraction numerator y minus 1 over denominator y end fraction$

Similarly, we can write z as
$z space equals space fraction numerator 1 over denominator 1 minus a b end fraction space rightwards double arrow a b space equals space fraction numerator z minus 1 over denominator z end fraction$

Multiply ab and equate the values and simplify

The correct answer is: yz+zx=xy+z

Given : $x equals sum subscript n equals 0 end subscript superscript infinity end superscript a to the power of n end exponent comma y equals sum subscript n equals 0 end subscript superscript infinity end superscript b to the power of n end exponent comma z equals sum subscript n equals 0 end subscript superscript infinity end superscript left parenthesis a b right parenthesis to the power of n end exponent$ , where a<1, b<1
To find : A relationship between x, y and z
We can write x as
$x space equals space fraction numerator 1 over denominator 1 minus a end fraction space rightwards double arrow a space equals space fraction numerator x minus 1 over denominator x end fraction$
Similarly, we can write y as
$y space equals space fraction numerator 1 over denominator 1 minus b end fraction space rightwards double arrow b space equals space fraction numerator y minus 1 over denominator y end fraction$

Similarly, we can write z as
$z space equals space fraction numerator 1 over denominator 1 minus a b end fraction space rightwards double arrow a b space equals space fraction numerator z minus 1 over denominator z end fraction$

$a space cross times space b space equals space open parentheses fraction numerator x minus 1 over denominator x end fraction close parentheses cross times space open parentheses fraction numerator y minus 1 over denominator y end fraction close parentheses space equals space open parentheses fraction numerator z minus 1 over denominator z end fraction close parentheses$
Solving the above, we get
$x y z space minus space x y space equals space left parenthesis x z minus z right parenthesis left parenthesis y minus 1 right parenthesis x y z space minus space space x y space equals space x y z space minus x z space minus z y space plus space z F u r t h e r space s i m p l i f y i n g comma space w e space g e t left parenthesis x y space plus space z right parenthesis space equals left parenthesis z x space plus y z right parenthesis$

Related Questions to study

If l, m, n are the $p to the power of text th end text end exponent comma q to the power of text th end text end exponent comma r to the power of text th end text end exponent$ terms of a G.P which are +ve, then $open vertical bar table attributes columnalign left end attributes row cell l o g invisible function application l end cell p 1 row cell l o g invisible function application m end cell q 1 row cell l o g invisible function application n end cell r 1 end table close vertical bar equals$

If l, m, n are the $p to the power of text th end text end exponent comma q to the power of text th end text end exponent comma r to the power of text th end text end exponent$ terms of a G.P which are +ve, then $open vertical bar table attributes columnalign left end attributes row cell l o g invisible function application l end cell p 1 row cell l o g invisible function application m end cell q 1 row cell l o g invisible function application n end cell r 1 end table close vertical bar equals$

The relationship between force and position is shown in the figure given (in one dimensional case) calculate the work done by the force in displacing a body from x=0 cm to x=5 cm

The relationship between force and position is shown in the figure given (in one dimensional case) calculate the work done by the force in displacing a body from x=0 cm to x=5 cm

physics-General

Fifth term of G.P is 2 The product of its first nine terms is

Fifth term of G.P is 2 The product of its first nine terms is

parallel

If a, b, c are in A.P then $a open parentheses fraction numerator 1 over denominator b end fraction plus fraction numerator 1 over denominator c end fraction close parentheses$ , $b open parentheses fraction numerator 1 over denominator c end fraction plus fraction numerator 1 over denominator a end fraction close parentheses comma c open parentheses fraction numerator 1 over denominator a end fraction plus fraction numerator 1 over denominator b end fraction close parentheses$ are in

If a, b, c are in A.P then $a open parentheses fraction numerator 1 over denominator b end fraction plus fraction numerator 1 over denominator c end fraction close parentheses$ , $b open parentheses fraction numerator 1 over denominator c end fraction plus fraction numerator 1 over denominator a end fraction close parentheses comma c open parentheses fraction numerator 1 over denominator a end fraction plus fraction numerator 1 over denominator b end fraction close parentheses$ are in

The ultimate source of organic evolution is

The ultimate source of organic evolution is

If $a subscript 1 end subscript comma a subscript 2 end subscript comma a subscript 3 end subscript horizontal ellipsis horizontal ellipsis horizontal ellipsis a subscript n end subscript$ are in A.P with common difference $d$ then sind $open square brackets c o s e c invisible function application a subscript 1 end subscript c o s e c invisible function application a subscript 2 end subscript plus close$ $c o s e c invisible function application a subscript 2 end subscript c o s e c invisible function application a subscript 3 end subscript plus c o s e c invisible function application a subscript 3 end subscript c o s e c invisible function application a subscript 4 end subscript plus horizontal ellipsis horizontal ellipsis n$ terms] $equals$

If $a subscript 1 end subscript comma a subscript 2 end subscript comma a subscript 3 end subscript horizontal ellipsis horizontal ellipsis horizontal ellipsis a subscript n end subscript$ are in A.P with common difference $d$ then sind $open square brackets c o s e c invisible function application a subscript 1 end subscript c o s e c invisible function application a subscript 2 end subscript plus close$ $c o s e c invisible function application a subscript 2 end subscript c o s e c invisible function application a subscript 3 end subscript plus c o s e c invisible function application a subscript 3 end subscript c o s e c invisible function application a subscript 4 end subscript plus horizontal ellipsis horizontal ellipsis n$ terms] $equals$

parallel

The sum of all integers between 50 and 500 which are divisible by 7 is

The sum of all integers between 50 and 500 which are divisible by 7 is

$left parenthesis 666 horizontal ellipsis text n digits end text right parenthesis squared plus left parenthesis 888 horizontal ellipsis n$ digits )=

$left parenthesis 666 horizontal ellipsis text n digits end text right parenthesis squared plus left parenthesis 888 horizontal ellipsis n$ digits )=

In a $increment blank P Q R$ as shown in figure given that $x colon y colon z equals 2 colon 3 colon 6$ , then the value of $angle Q P R$ is

In a $increment blank P Q R$ as shown in figure given that $x colon y colon z equals 2 colon 3 colon 6$ , then the value of $angle Q P R$ is

parallel

A bob of mass M is suspended by a massless string of length L. The horizontal velocity $v$ at position A is just sufficient to make it reach the point B. The angle $theta$ at which the speed of the bob is half of that at A, satisfies

A bob of mass M is suspended by a massless string of length L. The horizontal velocity $v$ at position A is just sufficient to make it reach the point B. The angle $theta$ at which the speed of the bob is half of that at A, satisfies

physics-General

A particle of mass $m$ attracted with a string of length $l$ is just revolving on the vertical circle without slacking of the string. If $v subscript A end subscript comma v subscript B end subscript$ and $v subscript D end subscript$ are speed at position $A comma B$ and $D$ then

A particle of mass $m$ attracted with a string of length $l$ is just revolving on the vertical circle without slacking of the string. If $v subscript A end subscript comma v subscript B end subscript$ and $v subscript D end subscript$ are speed at position $A comma B$ and $D$ then

physics-General

A bob of mass $M$ is suspended by a massless string of length $L$ . The horizontal velocity $V$ at position $A$ is just sufficient to make it reach the point $B$ . The angle $theta$ at which the speed of the bob is half of that at $A$ , satisfies

A bob of mass $M$ is suspended by a massless string of length $L$ . The horizontal velocity $V$ at position $A$ is just sufficient to make it reach the point $B$ . The angle $theta$ at which the speed of the bob is half of that at $A$ , satisfies

physics-General

parallel

A body of mass $m$ is moving with a uniform speed $v$ along a circle of radius $r$ , what is the average acceleration in going from $A$ to $B$ ?

A body of mass $m$ is moving with a uniform speed $v$ along a circle of radius $r$ , what is the average acceleration in going from $A$ to $B$ ?

physics-General

Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component, highest first

Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component, highest first

Physics-General

A boy throws a cricket ball from the boundary to the wicket-keeper. If the frictional force due to air cannot be ignored, the forces acting on the ball at the position X are respected by

A boy throws a cricket ball from the boundary to the wicket-keeper. If the frictional force due to air cannot be ignored, the forces acting on the ball at the position X are respected by

physics-General

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.