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Sometime I need to return some fraction equation to a geometric series and the above equation is one of them.

Can anyone help me?

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Hint: write $$ \frac1{4-x} = \frac 14\frac 1{1-\frac x4} $$

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  • $\begingroup$ ok thank you very much, the idea reached to me $\endgroup$ – E.H.E Oct 28 '14 at 12:48
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    $\begingroup$ do not forget to accpet the answer if it helped! $\endgroup$ – mookid Oct 28 '14 at 12:50
  • $\begingroup$ it is correct ,when |x|<4 $\endgroup$ – Khosrotash Oct 28 '14 at 12:51
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    $\begingroup$ @daryakhosrotash this is always correct, as long as you don't write the series expansion! $\endgroup$ – mookid Oct 28 '14 at 12:57
  • $\begingroup$ if |x|>4, you factorize by x and develop anyway (the reason will be $\frac{4}{x}$) :) $\endgroup$ – mvggz Oct 28 '14 at 13:11
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Yes You can. But with some restrictions$$\text{for}\quad |x|\lt4 $$

$$\frac1{4-x} =\left(\frac {\frac{1}{4}}{1-\frac x4}\right)=\frac{1}{4}+\frac{x}{4^2}+\frac{x^2}{4^3}+\cdots+\frac{x^r}{4^{r+1}}+\cdots$$

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  • $\begingroup$ Is there a problem ?? $\endgroup$ – E.H.E Oct 28 '14 at 12:54
  • $\begingroup$ I am a new user, so I don't know the law of this site. $\endgroup$ – E.H.E Oct 28 '14 at 12:57

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