# Thread: taylor series word problem

1. ## taylor series word problem

the nth derivative of f at x=1 is given by:

$f^{(n)}(1)= \frac{(n+2)!}{2^n}$

for n≥1 and f(1)=2. write the first 5 terms and the general term of the taylor series for f about x=1

2. Originally Posted by yoman360
the nth derivative of f at x=1 is given by:

$f^{(n)}(1)= \frac{(n+2)!}{2^n}$

for n≥1 and f(1)=2. write the first 5 terms and the general term of the taylor series for f about x=1
general term for a taylor series centered at x = 1 ...

$\frac{f^{(n)}(1) (x-1)^n}{n!}$

... so build it.