# Series Convergent/Divergent

• Mar 10th 2009, 11:41 PM
wilcofan3
Series Convergent/Divergent
Determine whether the series $\sum_{n=1}^{\infty} ln(n+\frac {1} {n} )- ln (n)$ converges or diverges.

I'm really bad with series. (Speechless)
• Mar 11th 2009, 05:37 AM
mr fantastic
Quote:

Originally Posted by wilcofan3
Determine whether the series $\sum_{n=1}^{\infty} ln(n+\frac {1} {n} )- ln (n)$ converges or diverges.

I'm really bad with series. (Speechless)

Note that $\ln \left( n+ \frac{1}{n} \right) - \ln (n) = \ln \left(1 + \frac{1}{n^2} \right) < \frac{1}{n^2}$ for $n \geq 1 \, ....$