Infinite series

**Dragonkiller** · August 5th 2012, 04:59 AM

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

**Prove It** · August 5th 2012, 05:04 AM

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...

**HallsofIvy** · August 5th 2012, 06:53 AM

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.

Thread: Infinite series

LinkBack

Thread Tools

Display

Infinite series

Re: Infinite series

Re: Infinite series

Similar Math Help Forum Discussions

[SOLVED] Fourier series to calculate an infinite series

Sum of an infinite series - comparing with a known series

Does convergence of an infinite series imply convergence of the infinite sequence?

Euler-Maclaurin Series formula on an infinite series?

calculus II areas about axis, pressure, infinite series, MacLaurin series

Search Tags