How do you find a power series representation for $f(x)=xln(x+1)$ and what is the radius of convergence?

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Answer 1 · 2016-06-28T06:01:58

$x^2- x^3/2+x^4/3-...+(-1)^(n-1)x^n/n+..., -1 < x<=1$

Power series for $x ln(x+1)$

$=x$ (power series for $ln(x+1)$

$=x(x-x^2/2+x^3/3-...), -1< x<=1$

$x^2-x^3/2+x^4/3-...+(-1)^(n-1)x^n/n+..., -1 < x<=1$

How do you find a power series representation for f(x)=xln(x+1)f(x)=xln(x+1) and what is the radius of convergence?