Answer Happy

Answers are given below. i just want steps.
DivergenCE TEST: Consider the series n=1∑∞​an​. If n→∞lim​an​=0 or does not exist, then the series diverges. In problems 1 (a-f)apply the Divergence Test (aka Divergence Theorem) to state that the series diverges, if applicable. (a) n=1∑∞​n1​ Divergence test not applicable; no information from divergence test (b) n=1∑∞​5n2+4n2​ Diverges by the divergence test (c) n=1∑∞​n(n+1)1​. Divergence test not applicable; no information from divergence test (d) (⋆)n=1∑∞​ln(2n+5n​) Diverges by the divergence test (e) n=1∑∞​arctann Diverges by the divergence test (f) Show that n=1∑∞​n1​ diverges using partial sums. (Refer to the lecture on Series to see the details.) Observe that S2n​>1+2n​.