Toronto Math Forum
MAT3342018F => MAT334Lectures & Home Assignments => Topic started by: Nikki Mai on November 19, 2018, 09:37:13 PM

Can anyone help me with 2.2 question11?
I am not sure how to solve with the hint.

$\frac{1}{4z}=\frac{1}{4}\frac{1}{1\frac{z}{4}}$
$\frac{1}{4z}=\frac{1}{4}\sum_{n=0}^{\infty}(\frac{z}{4})^n$
Take derivatives on both sides, then
$\frac{1}{(4z)^2}=\sum_{n=1}^{\infty}\frac{1}{4^{n+1}}nz^{n1}$ (Here, use the hint)
$\frac {z^2}{(4z)^2}=\sum_{n=1}^{\infty}\frac{1}{4^{n+1}}nz^{n+1}$
$=\sum_{n=1}^{\infty}n(\frac{z}{4})^{n+1}$
OK Fiexd it.

$\frac{1}{4^{n+1}}$ cannot be outside of the sum