Recent content by Saknussemm

The logic and context are not the same, as I was answering the question whether you can use the Taylor series. In general, you prove the validity of the Taylor expansion over a given interval by proving the Taylor reminder tends to zero as n goes to infinity. But here, because we can bring out a...

Taking the derivative of the MacLaurin series gives you $1 -x +x^2 - x^3 + x^4 + \ldots$ Since this is a geometric series with ratio $-x$, it equals $\frac{1}{1 + x}$ when x is in $(-1, 1)$. This shows the expression $\ln(1+x)$ and its MacLaurin expansion to have the same derivative over $(-1...