Consider the series:
1-1/2 -1/3 +1/4 +1/5 -1/6 -1/7........where the signs come in pairs. Does the series converge or diverge?
I want to use the alternating series test....any ideas? how I would solve this.
Thanks
As I said add them to gether in pairs. Write it out and you will see.
$\displaystyle a_1+a_2=1-\frac{1}{2}=\frac{1}{2}=b_1$
$\displaystyle a_3+a_4=-\frac{1}{3}+\frac{1}{4}=-\frac{1}{12}=b_2$
$\displaystyle a_5+a_6=\frac{1}{5}-\frac{1}{6}=\frac{1}{30}=b_3$
Note this is the series listed above I just gave the general term.
Since
$\displaystyle \sum a_n =\sum b_n$ we can look at the new series to draw any needed conclusions.