Show that $\sum^{\infty}_{n=1}\frac{(-1)^n}{n}$ converges.

Question

Show that $\displaystyle\sum^{\infty}_{n=1}\frac{(-1)^n}{n}$ converges.

Hint: consider the sum of two subsequent entries.

How can I use that hint to solve the questaion.. ?

$\frac{1}{2n-1}-\frac{1}{2n} = \frac{?}{(2n-1)(2n)} < \frac{?}{2n^2}$ — reuns, Mar 31 '17 at 02:34

score 0 · Answer 1 · answered Mar 31 '17 at 03:18

0

Hint: $1/n - 1/(n+1) = 1/[n(n+1)].$ That shows that if you group this series in pairs, it converges (by the comparison test). You still have some work left to do.

answered Mar 31 '17 at 03:18

zhw.

105,693

I got it !!! I solved it. Thank you – Hidoinggood Mar 31 '17 at 04:45

Show that $\sum^{\infty}_{n=1}\frac{(-1)^n}{n}$ converges.

1 Answers1