Question

Find a power series for f(x)=xln(1+x). \[f(x)=xln(1+x)\]. \[\frac{d}{dx}xln(1+x)\]. \[=\frac{x}{x+1}+ln(x+1)\]. \[=\sum_{n=0}^{\infty}(-1)^nx^n+\frac{d}{dx}ln(x+1)\]. \[\sum_{n=0}^{\infty}(-1)^nx^n+\sum_{n=0}^{\infty}(-1)^n\frac{x^{n+1}}{n+1}\]

Answer 1

In your question that first im confused but i arrange if correctly though, in my calculation the possible power of the series is infinity ∑ n-0 times the -1 one to the power of n over n+1 times x to the power of n+2