Math Help - converge and diverge problem

1. converge and diverge problem

Does this problem converge absolutely, conditionally, or does it diverge?

the equation: [url=http://img219.imageshack.us/img219/5968/untitled7gf.jpg[/url]

also, the hint is to first show that ln(1 + x) <= x if x > 0

Thanks for any help.

2. Originally Posted by rcmango
Does this problem converge absolutely, conditionally, or does it diverge?

the equation: [url=http://img219.imageshack.us/img219/5968/untitled7gf.jpg[/url]

also, the hint is to first show that ln(1 + x) <= x if x > 0

Thanks for any help.
As the term inside the log is monotonicaly decreasing and goes to 1 as n
goes to infinity, the log term is monotonicaly decreasing and goes to zero,
thus by the alternating series test the series converges. See the other