# Show that a series converges

1. Feb 11, 2010

### soopo

1. The problem statement, all variables and given/known data
The series is at http://img203.imageshack.us/i/snapshot1g.png/

3. 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.

2. Feb 11, 2010

### 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.

3. Feb 12, 2010

### Ratio Test =)

Its a riemann sum.

4. Feb 12, 2010

### owlpride

^ Clever! I missed the obvious.