The Taylor series about x=5 for a certain function f converges to f(x) for all x in the interval of convergence. The nth derivative of f at x=5 is given by fn(5)=[(-1)^n x n!]/[2^n x (n + 2)], and f(5)=1/2.
The fn above should be "f to the nth derivative."
a)Write the third-degree Taylor polynomial for f about x=5.
b)Find the radius of convergence of the Taylor series for f about x=5.

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The Taylor series expansion would be,\[\sum_{n=0}^{\infty}=\frac{(-1)^n}{2^n(n+2)}(x-5)^n\]

You need to expand this up to the third power; that is, from n=0 to 3.

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