1. Summing Infinite Series Questions

How to sum this series?

$\sum_{n=0}^{\infty} \left( \left(\frac{1}{2}+\frac{1}{\sqrt{5}}\right)^n + \left(\frac{1}{2}-\frac{1}{\sqrt{5}}\right)^n \right)$

2. Note that

$\displaystyle \sqrt{5}>2 \implies \frac{1}{2}\pm \frac{1}{\sqrt{5}}<1$

So just break the the series into two parts they are both geometric and remember that

$\displaystyle \sum_{n=0}^{\infty}r^n=\frac{1}{1-r}$

3. Thank you very much, the answer came out to be 20