Question

Find the Taylor series of f(x)=ln(1+2x) around x_0=1

Answer 1

this doesn't look fun
around \(1\) ?

Answer 2

constant is \(f(1)=\ln(3)\)

Answer 3

the derivative is
\[\frac{2}{1+2x}\] at \(1\) you get \(\frac{2}{3}\) so the next term is
\[\frac{2}{3}(x-1)\]

Answer 4

how do we write the taylor series