Question

Find the Taylor series for f centered at 5 if f^(n)(5) = ((-1)^n n!) / (4^n(n + 3)) sum_{n=0}^{infinity} ( What is the radius of convergence R of the Taylor series? R =

          Find the Taylor series for f centered at 5 if
f^(n)(5) = ((-1)^n n!) / (4^n(n + 3))

sum_{n=0}^{infinity} (

What is the radius of convergence R of the Taylor series?
R =

Added by Victor Manuel C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

05/11/2023

Step 1

The Taylor series is given by: $$f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(5)}{n!}(x-5)^n$$ We are given that $f^{(n)}(5) = (-1)^n 4^n (n+3)$. So, the Taylor series becomes: $$f(x) = \sum_{n=0}^{\infty} \frac{(-1)^n 4^n (n+3)}{n!}(x-5)^n$$ Now, we need to find Show more…

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