Determine whether the series summation (n=0 to infinity) (-1)^n /(5n+1) is absolutely convergent,

conditionally convergent, or divergent.

i know that to be absolutely convergent then summation |a sub n| is convergent

then |a sub n| = 1/(5n+1) but i'm not sure what test to apply here? is it still an alternating series?

Limit comparison test with ∑ a(n) =∑1/n : lim(b(n)/a(n)= lim {(1/(5n+1)}/(1/n)=lim(1/(5+1/n) (as n→∞) = 1/5, where 0<1/5<∞. Hence the two series both converge or both diverge. But ∑1/n diverges (standard divergent series). Hence ∑1/(5n+1) diverges and ∑(-1)^n{1/(5n+1)} is not absolutely convergent. It is however conditionally convergent by the alternating series test because b(n)=1/(5n+1)>0 (all n), (2)b(n+1)≤b(n) and (3) b(n)→0 as n→∞.