What is the sum of 2 to infinity of 2/(n^2-1)?

Question

http://i167.photobucket.com/albums/u141/SitrONes7/2-1.jpg

Answer 1

2/(n² - 1) = 1/(n-1) - 1/(n+1)

then the sum is :

S = 1/1 - 1/3 + 1/2 - 1/4 + 1/3 - 1/5 + 1/4 - 1/6 + 1/5 - 1/7 + ...

S = 1 + 1/2 + (1/3 - 1/3) + (1/4 - 1/4) + (1/5 - 1/5) + ...
S = 1+ 1/2 = 3/2

Answer 2

Square

here is the fromula

N = (x^2 + y^2)/(1+xy)
x^2 + y^2
--------- = N
1 + xy
If the number (a^2 + b^2)/(1+a*b) with a,b integers is a positive
integer, then it is a perfect square. (The stipulation of *positive*
integer is required, because we have integers a=1, b=-2 such that
(a^2 + b^2)/(1+ab) equals the integer -5, but this is not a perfect
square.) To prove this, first note that, for any positive integer
N, if the equation

-bry