quasar987
Nov29-04, 05:59 PM
Hi. I am starting the study of series and I don't see how to do this problem.
"Show that
\sum_{n=0}^\infty \frac{1}{(n+a)(n+1+a)} = \frac{1}{a}"
All i got is the decomposition in partial fractions as
\sum_{n=0}^\infty (...) = \sum_{n=0}^\infty \frac{1}{(n+a)} + \sum_{n=0}^\infty \frac{-1}{(n+1+a)}
if these sum converge. I tried seeing a patern in the partial sums to find S_n but it's too difficult so there must be another way.
Any hint/help will be appreciated.
"Show that
\sum_{n=0}^\infty \frac{1}{(n+a)(n+1+a)} = \frac{1}{a}"
All i got is the decomposition in partial fractions as
\sum_{n=0}^\infty (...) = \sum_{n=0}^\infty \frac{1}{(n+a)} + \sum_{n=0}^\infty \frac{-1}{(n+1+a)}
if these sum converge. I tried seeing a patern in the partial sums to find S_n but it's too difficult so there must be another way.
Any hint/help will be appreciated.