For what value of real constant $a$ does the following series converge?
$$
1+(1/\sqrt{3})-(a/\sqrt{2})+(1/\sqrt{5})+(1/\sqrt{7})-(a/\sqrt{4})+(1/\sqrt{9})+(1/\sqrt{11})-(a/\sqrt{6})...
$$
I do not have a clue on how to proceed. Suggest a possible route.

can we do it by comparison test somehow? Can we comapre it with $c/\sqrt{(n)}$ for some $c$ and some large enough $n$?