# Uniform Convergence of a series

• Jan 4th 2013, 12:22 PM
problem
Uniform Convergence of a series
Show that the series $\sum_{n=1}^\infty \left(\frac{x}{n}-ln(1+\frac{x}{n})\right)$ converges uniformly on $(-1,A)$ for $A>-1$ and that the sum of the series has derivatives of all orders on $(-1,\infty)$.