Home
Class 11
MATHS
If (1)/(1^(2))+(1)/(2^(2))+(1)/(3^(2))+c...

If `(1)/(1^(2))+(1)/(2^(2))+(1)/(3^(2))+cdots "to" oo = (pi^(2))/(6) ` then `(1)/(1^(2)) +(1)/(3^(2))+(1)/(5^(2))+cdots` equals

A

`pi^(2) //8`

B

`pi^(2)//12`

C

`pi^(2)//3`

D

`pi^(2)//2`

Text Solution

Verified by Experts

Promotional Banner

Similar Questions

Explore conceptually related problems

1 (1)/(2) xx 6 (2)/(3)

int ( sqrt ( 5 + x ^(2)))/( x ^(4)) dx is equal to a) (1)/(15) (1 + (5)/( x ^(2)) ) ^((3)/(2)) b) (-1)/( 15) (1 + ( 1)/( x ^(2))) ^((3)/(2)) +C c) (-1)/( 15) (1 + (5)/(x ^(2))) ^((3)/(2))+ C d) (1)/(15) (1 + (1)/( x ^(2))) ^((3)/(2)) +C

For x gt 0 the sum of the series (1)/(1+x) - ((1-x))/((1+x)^(2))+ ((1-x)^(2))/((1+x)^(3))- cdots oo is equal to

If y=tan^(-1)((4x)/(1+5x^(2)))+tan^(-1)((2+3x)/(3-2x)) , then (dy)/(dx) is equal to a) (5)/(1+25x^(2)) b) (1)/(1+25x^(2)) c)0 d) (5)/(1-25x^(2))

Find the sum 1+(1)/(1+2) + (1)/(1+2+3) + cdots+ (1)/(1+2+3+cdots+ n )

If H_(n) =1+(1)/(2)+ cdots + (1)/(n) then value of S_(n) =1 + (3)/(2) + (5)/(3) +cdots + (2n-1)/(n) is

Find the sum 1^(2) + (1^(2)+2^(2))+ (1^(2)+2^(2)+3^(2))+ cdots up to 22 nd term.

If S = (2^(2)-1)/(2)+(3^(2)-2)/(6)+(4^(2)-3)/(12)+ cdots upto 10 terms then S is equal to

lim_(n to infty)(1^(2)/(1-n^(3))+2^(2)/(1-n^(3))+…+n^(2)/(1-n^(3))) is equal to :

The sum to n terms of the series 1+2 (1+(1)/(n))+3 (1+(1)/(n))^(2)+ cdots is given by