# Math Help - Infinite series

1. ## Infinite series

Hi, just wondering if anyone can help me with a quick infinite series question:
Show that this series diverges: $\sum_{n=1}^{\infty }\frac{2}{n}-\frac{1}{2^n}$
Thanks

2. ## Re: Infinite series

Originally Posted by Dragonkiller
Hi, just wondering if anyone can help me with a quick infinite series question:
Show that this series diverges: $\sum_{n=1}^{\infty }\frac{2}{n}-\frac{1}{2^n}$
Thanks
The Harmonic Series is divergent...

3. ## Re: Infinite series

You know, or should know, that $\sum \frac{1}{2^n}$ converges- it is a geometric series and there is a simple formula for its sum.
IF the given sum converged, then we could write $2\sum\frac{1}{n}= \sum\left(\frac{2}{n}- \frac{1}{2^n}\right)+ \sum \frac{1}{2^n}$ but, as Prove It said, the series on the left does not converge.