Find the Taylor series generated by f at x = a.
-$$f ( x ) = \frac { 1 } { 9 - x } , a = 7$$
A) $\sum _ { n = 0 } ^ { \infty } \frac { ( x - 7 ) ^ { n + 1 } } { 2 ^ { n } }$
B) $\sum _ { n = 0 } ^ { \infty } \frac { ( x - 7 ) ^ { n } } { 2 ^ { n + 1 } }$
C) $\sum _ { n = 0 } ^ { \infty } \frac { ( x - 7 ) ^ { n + 1 } } { 2 ^ { n + 1 } }$
D) $\sum _ { n = 0 } ^ { \infty } \frac { ( x - 7 ) ^ { n } } { 2 ^ { n } }$

Question

Quizplus · Accepted Answer

The function can be rewritten as $f(x) = \frac{1}{2 - (x - 7)}$, which is a geometric series with a first term of $1/2$ and a common ratio of $(x - 7)/2$. The Taylor series is therefore $\sum_{n=0}^{\infty} \frac{(x - 7)^n}{2^{n+1}}$, matching option B.

Find the Taylor Series Generated by F at X = f(x)=19−x,a=7f ( x ) = \frac { 1 } { 9 - x } , a = 7f(x)=9−x1​,a=7

Find the Taylor Series Generated by F at X = $f ( x ) = \frac { 1 } { 9 - x } , a = 7$