Maclaurin Series: Find a_n for f(x) = 1/(1+3x)

[Kuno]

Homework Statement

find $$a_{n}$$ for $$f(x)\ =\ \frac{1}{1+3x}$$

The Attempt at a Solution

I got:
f(0) = 1
f'(0) = -3
f''(0) = 9

The answer I ended up with was:
$$a_{n} \ = \ {(-1)}^n\frac{3^n}{n!}$$

However, the answer in the back of my book has the same answer except it's not divided by n!.

 

[truewt]

the n! is canceled out somehow. Recheck your workings.

Hint: Find f^n(x). I don't know what's the notation for the nth derivative of f(x)

 

[Kuno]

Okay I see it now, thanks.

 

[truewt]

you're welcome :)