Hi there,

I was wondering if you guys could be able to find the sum of the following series:

$S = 1/((1\cdot2)^2) + 1/((3\cdot4)^2) + 1/((5\cdot6)^2) + ... + 1/((n\cdot(n+1))^21/(((2n-1)\cdot2n)^2)$, in which ${n\to\infty}$ .

This question came to mind when I was looking at this (http://www.stat.purdue.edu/~dasgupta/publications/tr02-03.pdf) paper by Professor Anirban DasGupta. In the last section, a couple of specific examples of his 'unified' method to find the sums of infinite series is pressented. In equation (34), he states that the following series:

$1/(1\cdot2) + 1/(3\cdot4) + 1/(5\cdot6) + ... 1/(n\cdot(n+1)1/(2n\cdot(2n-1)) = log(2)$ (Note that ${n\to\infty}$ again). I was wondering If it's possible to find the sum if the values of the denominators of the terms are squared.

Max Muller

3 corrected spelling

Hi there,

I was wondering if you guys could be able to find the sum of the following series:

$S = 1/((1\cdot2)^2) + 1/((3\cdot4)^2) + 1/((5\cdot6)^2) + ... + 1/((n\cdot(n+1))^2)$, in which ${n\to\infty}$ .

This question came to mind when I was looking at this (http://www.stat.purdue.edu/~dasgupta/publications/tr02-03.pdf) paper by Professor Anirban DusGuptaDasGupta. In the last section, a couple of specific examples of his 'unified' method to find the sums of infinite series is pressented. In equation (34), he states that the following series:

$1/(1\cdot2) + 1/(3\cdot4) + 1/(5\cdot6) + ... 1/(n\cdot(n+1)) = log(2)$ (Note that ${n\to\infty}$ again). I was wondering If it's possible to find the sum if the values of the denominators of the terms are squared.

Max Muller

2 deleted 1 characters in body

Hi there,

I was wondering if you guys could are be able to find the sum of the following series:

$S = 1/((1\cdot2)^2) + 1/((3\cdot4)^2) + 1/((5\cdot6)^2) + ... + 1/((n\cdot(n+1))^2)$, in which ${n\to\infty}$ .

This question came to mind when I was looking at this (http://www.stat.purdue.edu/~dasgupta/publications/tr02-03.pdf) paper by Professor Anirban DusGupta. In the last section, a couple of specific examples of his 'unified' method to find the sums of infinite series is pressented. In equation (34), he states that the following series:

$1/(1\cdot2) + 1/(3\cdot4) + 1/(5\cdot6) + ... 1/(n\cdot(n+1)) = log(2)$ (Note that ${n\to\infty}$ again). I was wondering If it's possible to find the sum if the values of the denominators of the terms are squared.