Home
Class 12
MATHS
Find the sum Sigma(r=1)^(oo)(3n^2+1)/((n...

Find the sum `Sigma_(r=1)^(oo)(3n^2+1)/((n^2-1)^3)`

Text Solution

Verified by Experts

The correct Answer is:
`9/16`
`T_(n)=(3n^(2)+1)/((n^(2)-1)^(3))=1/2(6n^(2)+2)/((n^(2)-1)^(3))`
`=1/2(((n+1)^(3)-(n-1)^(3))/((n+1)^(3)(n-1)^(3)))`
`=1/2(1/((n-1)^(3))-1/(n+1)^(3))`
`thereforeS=1/2[(1/1^(3)-1/3^(3))+(1/2^(3)-1/3^(3))+(1/2^(3)-1/4^(3))+(1/3^(3)-1/5^(3))`
`+(1/4^(3)-1/6^(3))+...]`
`=1/2(1+1/8)=9/16`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise (Single)|93 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise (Multiple & Comprehension)|66 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.8|10 Videos

  • PROBABILITY II

    CENGAGE|Exercise JEE Advanced Previous Year|25 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

Find the sum Sigma_(r=1)^(oo) (r)/(r^4+1/4)

Find the sum Sigma_(r=1)^(oo) (r-2)/((r+2)(r+3)(r+4))

Find the sum Sigma_(r=1)^(n) 1/(r(r+1)(r+2)(r+3)) Also,find Sigma_(r=1)^(oo) 1/(r(r+1)(r+2)(r+3))

Find the sum sum_(r =1)^(oo) tan^(-1) ((2(2r -1))/(4 + r^(2) (r^(2) -2r + 1)))

Find the sum Sigma_(r=1)^(n) r/((r+1)!) . Also, find the sum of infinite terms.

Find the sum Sigma_(j=1)^(n) Sigma_(i=1)^(n) I xx 3^j

Find the sum sum_(r=1)^n r^2(^n C_r)/(^n C_(r-1)) .

Find the sum_(k=1)^(oo) sum_(n=1)^(oo)k/(2^(n+k)) .