Author Topic: 2.2 Q11  (Read 492 times)

Nikki Mai

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2.2 Q11
« 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.

Ye Jin

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Re: 2.2 Q11
« Reply #1 on: November 19, 2018, 09:59:15 PM »
    $\frac{1}{4-z}=\frac{1}{4}\frac{1}{1-\frac{z}{4}}$
    $\frac{1}{4-z}=\frac{1}{4}\sum_{n=0}^{\infty}(\frac{z}{4})^n$
   
   Take derivatives on both sides, then
    $\frac{1}{(4-z)^2}=\sum_{n=1}^{\infty}\frac{1}{4^{n+1}}nz^{n-1}$  (Here, use the hint)
   
    $\frac {z^2}{(4-z)^2}=\sum_{n=1}^{\infty}\frac{1}{4^{n+1}}nz^{n+1}$
             
              $=\sum_{n=1}^{\infty}n(\frac{z}{4})^{n+1}$


OK Fiexd it.
« Last Edit: November 20, 2018, 02:32:39 PM by Ye Jin »

Victor Ivrii

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Re: 2.2 Q11
« Reply #2 on: November 20, 2018, 06:24:15 AM »
$\frac{1}{4^{n+1}}$ cannot be outside of the sum