Generating Function

Question

How to apply this theorem to $\frac{x^{3}}{1-x}$ 

Comments

right answer is x³ +x⁴ +x⁵ +x⁶ +.......

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is x³ a power series? i'm really new to this topic but i think we cannot apply this theorem to this question

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ohh you follow this

Answer 1

G(x) = $x^{3}.\frac{1}{1-x}$

G(x) = $x^{3}[1+x+x^{2}+x^{3}+x^{4}+...............................]$     

G(x) = $x^{3}+x^{4}+x^{5}+x^{6}+.................................$

Comments

starting from x³

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actually i knew this but the problem is applying theorems with product of power series

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@Mk Utkarsh 

You see this 

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I'm not comfortable with theorem

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yeah but let's say f(x),g(x) = $\frac{1}{(1-x)^{2}}$

and we need to apply theorem that theorem on f(x)g(x) which is $\frac{1}{(1-x)^{4}}$

i know in table there is $\frac{1}{(1-x)^{n}}$ but still just for understanding

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ok i understand 
i asked here

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Yeah

But theorem looks like complicated for me

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How to make here button clickable ??

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link the text 

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Ok Thank

you see my doubt https://gateoverflow.in/205400/self-doubt-generating-function

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just started with generating functions maybe till the end of the day i might able to answer :p