Question

Would someone expand this using mclaurins?
(x+2)/(x−4)(x−2)

Answer 1

at x = 0?

Answer 2

yes

Answer 3

use partial fractions first

Answer 4

you need to split it up first

Answer 5

yeah i did that. 2/(2-x) - 3/(4-x)

Answer 6

A long division will give the McLauren series for the function.

Answer 7

then factor out the constants and use geometric series sum

Answer 8

better idea than what i was going to do for sure.

Answer 9

\[= \frac{ 2}{ 2 ( 1 - \frac{x}{2} ) } - \frac{3}{ 4 ( 1- \frac{x}{4} ) } \]

Answer 10

stucked after partial fraction. :( I dont want to do mclaurins separately.

Answer 11

\[=\sum_{n=0}^{\infty}[ (\frac{x}{2} ) ^n - \frac{3}{4} (\frac{x}{4})^n ]\]

Answer 12

you can simplify the sum a bit if you want

Answer 13

shouldn't the constant be 1/4? if i put n = 0 i get -1/4 here? not to interrupt because this all looks good

Answer 14

\[=\sum_{n=0}^{\infty} (1- \frac{ 3}{2^{n+2}} ) (\frac{x}{2})^n \]

Answer 15

think thats it, something similair