Let $\sum_{n=1}^{\infty}n^5(\frac{x}{x+2})^n=S(x)$. Prove that the sum S(x) is a function and continuous to $x\epsilon [0,10]$ Let $\sum_{n=1}^{\infty}n^5(\frac{x}{x+2})^n=S(x)$. Prove that the sum S(x) is a function and continuous to $x\epsilon [0,10]$
Since we are talking about sums and we need to prove continuous i directly thought about Uniform convergence.
But i can't see how to do it on this one, What's the idea?

Hint: For convergence, compare with $\displaystyle\sum_1^\infty n^5 \left(\frac{11}{12}\right)^n$. This can also be used to show uniform convergence in our inteval. (Irrelevant comment; the given series is not a power series.)
