Does 1/ln(x+1) converge or diverge?

I've tried the nth term test, limit comparison test, and integral test. All I get is inconclusive. The other tests I have (geometric series, p-series, telescoping series, alternating series, and root tests) don't apply. What can I use?!

As x-> infinity, 1/ln (x+1) approaches zero. That means that it converges.
Is that the limit you had in mind?

As x-> -1, it converges to zero
As x-> 0, it diverges, since ln 1 = 0
ln (x+1) is undefined for x<-1

No, I wondered if the sum converged, not the sequence. Sorry

asked by Mischa

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