Submit the quiz and homework during the final exam

Problem 1. Find the sum of the series $\displaystyle{\sum_{n=2}^{\infty}{\frac{2}{n(n+2)}}}$

Problem 2. Find the radius of convergence and interval of convergence of the series $\displaystyle{\sum_{n=1}^{\infty}{\frac{5^{n+1}{x^n}}{2n+1}}}$