But the series of a is ∑ 1/nlnn, which is obviously divergent.

C: the simplest, un = (-1) (n-1)/n.

∑un = 1- 1/2+ 1/3- 1/4+ ...

u2n- 1 = 1/(2n- 1)，u2n=- 1/2n

So the subtraction becomes1/(2n-1)+1/2n, and this series becomes (1+1/2)+(1/3+1). ...

Why does ∑ (1/(2n-1)+1/2n) diverge? I use the comparative convergence method.

1/(2n- 1)+ 1/2n & gt； 1/2n+ 1/2n = 1/n

And ∑ 1/n divergence, small divergence and large divergence.