We can simplify as follows: $$\frac{1}{x} + \frac{1}{x^2}+ \frac{1}{x^3}+...+\frac{1}{x^n}=\frac{x^{n-1}}{x^n} + \frac{x^{n-2}}{x^n}+ \frac{x^{n-3}}{x^n}+...+\frac{1}{x^n}=\frac{\overbrace{1+x+x^2+...+x^{n-1}}^{\text{geometric series}}}{x^n}$$
Recall the partial sum of a geometric series is $$\sum _{k=i}^{n}z^{k}={\frac {z^{i}-z^{n+1}}{1-z}}$$
You should be able to proceed.
Answer below.
