Question

\[\sum_{n=1}^{\infty} n(-1)^{n-1}\]=?

Answer 1

That series isn't going to converge. It's going to flop back and forth between positive and negative numbers on the addition of each successive term.

Answer 2

1+(-2)+3+(-4)+... will flip back and forth between + and - in other words.

Answer 3

if s is the sum of the series,
refer to the picture

Answer 4

what did you do??

Answer 5

jz a mystery....

Answer 6

the sum shouldn't converge even if you use telescoping
there is something fishy ...
http://www.wolframalpha.com/input/?i=sum%5Bn%28-1%29%5E%28n%2B1%29%2Cn%2C1%2Cinf%5D

Answer 7

It's telescoping outward, not inward. It diverges.

Answer 8

http://www.youtube.com/watch?v=kIq5CZlg8Rg
watch this

Answer 9

If
\[
\sum_1^\infty a_n
\]
is convergent then
\[
\lim a_n =0
\]
Which is not the case here.