Evaluating Summation of $5^{-n}$ from $n=4$ to infinity The answer is $\frac1{500}$ but I don't understand why that is so. 
I am given the fact that the summation of $x^{n}$ from $n=0$ to infinity is $\frac1{1-x}$. So if that's the case then I have that $x=\frac15$ and plugging in the values I have $\frac1{1-(\frac15)}= \frac54$.

The formula gives from $n=0$ to infinity, but you are asked to sum from $n=4$ to infinity. In this case, you take the terms from $n=0$ to infinity using the formula (which you determined is $\frac54$), and get rid of the extra terms. In this case, we don't need the terms when $n=0,1,2,3$, so we can get rid of those terms by subtracting them. The sum is then $\frac54-5^{-0}-5^{-1}-5^{-2}-5^{-3}=\frac1{500}$.
