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

Question

anonymous · Answer

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.

anonymous · Answer

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

cwtan · Answer

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

experimentx · Answer

what did you do??

cwtan · Answer

jz a mystery....

experimentx · Answer

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

anonymous · Answer

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

experimentx · Answer

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

anonymous · Answer

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