Question

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

Answer 1

what does c=1 mean

Answer 2

just a variable, thats where im actually lost

Answer 3

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

Answer 4

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

Answer 5

the top one 1/(4x-6)

Answer 6

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

Answer 7

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.

Answer 8

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