Show that the series converges

[soopo]

Homework Statement

The series is at http://img203.imageshack.us/i/snapshot1g.png/

The Attempt at a Solution

The LHS series diverges. However, the term 1/n seems to be make the series to converge.
However, I am not completely sure how to proceed in proving that the series converges.

I should first show that the series has a converging point.
Then I can show that the series converges.

 

[LCKurtz]

That isn't a series, it is a sequence.

$$a_n = \frac 1 n\left(\frac 1 2 + \frac 2 3 + ... + \frac n {n+1}\right)$$

One way to prove a sequence converges is to show it is bounded above and increasing. Try that.

 

[Ratio Test =)]

Its a riemann sum.

 

[owlpride]

^ Clever! I missed the obvious.

[/thread hijack]

 

[Dick]

Its a riemann sum.

I don't think it's really a Riemann sum. The kth term is (k/n)/(k+1). If it were a Riemann sum, that would be a function only of (k/n).