having problem with reindexing the series

[steveyip]

I am having problems to reindex the following sums so that the anwser of
subtracting the summation of n*(n+1)x^(n+1)(n=1...infinity)from
the summation of n*(n+1)x^(n)(n=1...infinity)
can be obtained

thanks for your help in advance
Jerry

[Serge Steer]

>I am having problems to reindex the following sums so that the anwser of
>subtracting the summation of n*(n+1)x^(n+1)(n=1...infinity)from
>the summation of n*(n+1)x^(n)(n=1...infinity)

>can be obtained.

Using Maple one can find that
sum(n*(n+1)*x^(n),n=1..infinity)-sum(n*(n+1)*x^(n+1),n=1..infinity);
equals to
2
x x
-2 -------- + 2 --------
3 3
(x - 1) (x - 1)

--
Serge Steer
Inria Rocquencourt
BP 105 78153 Le Chesnay CEDEX
email:Serge...@inria.fr