For the series sum(n=1)(inf) (-1)^n*a_n where a_n = 1/n when n is even

[ussscou]

For the series sum(n=1)(inf) (-1)^n*a_n where a_n = 1/n when n is even and 1/n^2 when n is odd, is it divergent?

 

[tiny-tim]

welcome to pf!

hi ussscou! welcome to pf!

tell us what you think (and why), and then we'll comment!

 

[mathman]

For the series sum(n=1)(inf) (-1)^n*a_n where a_n = 1/n when n is even and 1/n^2 when n is odd, is it divergent?

The even terms sum diverges, while the odd terms sum converges. Conclusion?