Hi, just wondering if anyone can help me with a quick infinite series question:
Show that this series diverges: $\displaystyle \sum_{n=1}^{\infty }\frac{2}{n}-\frac{1}{2^n}$
Thanks
You know, or should know, that $\displaystyle \sum \frac{1}{2^n}$ converges- it is a geometric series and there is a simple formula for its sum.
IF the given sum converged, then we could write $\displaystyle 2\sum\frac{1}{n}= \sum\left(\frac{2}{n}- \frac{1}{2^n}\right)+ \sum \frac{1}{2^n}$ but, as Prove It said, the series on the left does not converge.