# Infinite series

• Aug 5th 2012, 05:59 AM
Dragonkiller
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 :)
• Aug 5th 2012, 06:04 AM
Prove It
Re: Infinite series
Quote:

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...
• Aug 5th 2012, 07:53 AM
HallsofIvy
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.