## anonymous 5 years ago hi, im looking for some help on finding a power series f(x)=1/4x-6 centered a c=1

1. anonymous

what does c=1 mean

2. anonymous

just a variable, thats where im actually lost

3. anonymous

not exactly sure how to apply it to the equation, i have some examples but i cant math the answer on th review

4. apples

Do you mean $\frac{1}{4x-6}$ or $\frac{1}{4x} - 6$

5. anonymous

the top one 1/(4x-6)

6. apples

$\frac{1}{4x-6} = \frac{1}{4} \cdot \frac{1}{x - \frac{3}{2}} = -\frac{1}{4} \cdot \frac{1}{\frac{3}{2} - x} = -\frac{1}{4} \cdot \frac{2}{3} \cdot \frac{1}{1 - \frac{2x}{3}} = -\frac{1}{6} \cdot \frac{1}{1 - \frac{2x}{3}}$ using the definition of the geometric series, we arrive at $-\frac{1}{6} \sum_{n = 0}^{\infty} \left(\frac{2x}{3} - 1\right)^n$

7. anonymous

well thank you sir, i will go ahead and follow ur example and try to see if ai can do a few problems thank you.

8. apples

A note: If it's centered at c = a, then you just use (x - a) as your term.