# Can I return the $\frac{1}{4-x}$ to a geometric series?

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

Can anyone help me?

## 2 Answers

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

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

Yes You can. But with some restrictions$$\text{for}\quad |x|\lt4$$

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

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