Question

级数的敛散性级数如下图,判断其是否收敛,如果收敛是条件收敛还是绝对收敛?

Answer 1

i think it is convergent and it converges absoluely.

we use the alternating series test, that is if |fn| is decreasing and the limit of |fn|=0 when n->infinity ,then the series of fn is absolutely convergent.

|fn|=1/(nln(n+1)) which is decreasing obviously and equals 0 when n approaches infinity.