Question

How to find if the sum converges or diverges (-1)^n /nln(n)

Answer 1

#1 Do the individual terms vanish? Do they approach zero?
If not, then it diverges.
If so, then it might converge.

What say you?

Answer 2

the limit approaches 0 I guess because ln(infinity) is infinity

Answer 3

Okay, now part two.

Do you have an IMPRESSION as to whether it diverges or converges?

Answer 4

converges?

Answer 5

That's good. Alternating Series are trivial. If it is alternating, all you need is part 1.

Notice how the harmonic series diverges: 1 + 1/2 + 1/3 + 1/4 + ...
But the alternating harmonic series converges: 1 - 1/2 + 1/3 - 1/4 + ...

Proof:
1) Individual Terms Vanish
2) Alternating Series
3) Converges.
Done!

Answer 6

so it is conditionally convergent?

Answer 7

Like the Alternating Harmonic Series, yes.