SUM n=2_infinity (2)/(n^2 - 1)
does this series converge or diverge?
also, find its sum.
Please help me with this problem. Also can u identify what type of series it is.
thankyou.
2/(n+1)(n-1) = 1/(n-1) - 1/(n+1)
This is a "Telescoping Series" write out the partial sums.
S_2=1/1 - 1/3
S_3=1/1-1/3+1/2-1/4 = 1+1/2-1/3-1/4
S_4=1/1-1/3+1/2-1/4+1/3-1/5 = 1+1/2 - 1/4-1/5
...
It seems the general pattern is,
S_n= 1+1/2 - 1/n - 1/(n+1) for n>=2
Take n--> +oo
To find its sum.