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The sum to infinity of the series 3/1.2²+5/2².3²+7/3².4²+........ You haven't answered my 2questions.I posted before 4days. Plz answer............. .

The sum to infinity of the series 3/1.2²+5/2².3²+7/3².4²+........
 
 
You haven't answered my 2questions.I posted before 4days. Plz answer.............
.

Grade:11

1 Answers

Aditya Gupta
2086 Points
5 years ago
nth term is 
an= (2n+1)/(n^2*(n+1)^2)= 1/n^2 – 1/(n+1)^2.....[note that we are using telescopic sum method to solve the question here]
so, if we let f(n)=1/n^2, then an= f(n) – f(n+1)
now, sum= f(1)-f(2)+f(2)-f(3)+.....
=f(1)-f(infinty)=f(1)-0
=f(1)=1/1^2
=1

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