Taylor's Theorem

1. Apr 9, 2006

factor

I'm computing the minimum number of terms for a Taylor polynomial to approximate f(1.5) within .0001 where f(x) = ln(x + 1) using Taylor's theorem, but I'm having a little trouble getting there. I keep coming up with the absolute value of the (n+1)th derivative of ln(x + 1) as (n!)/[(x+1)^(n+1)] in which case the largest value for any derivative of ln(x + 1) from 0 to x would be n! but if I use this with Taylor's Theorem I get (n!)[(1.5)^(n+1)] / (n+1)! < .0001 but this is not true for any n. Any help would be appreciated.

Last edited: Apr 9, 2006
2. Apr 10, 2006

HallsofIvy

Did you forget the 1/n! in Taylor's formula?

3. Apr 10, 2006

benorin

Since the series is a alternating, why not use "the absolute value of the error is less than the absolute value of the first term omitted"?

4. Apr 10, 2006

factor

Well that's the problem benorin, I'm not looking for just the error, I already know what it should be. I'm looking for the term at which the error is less than .00001. In the case of the other post, even if I multiply by 1/n! I'm simply left with 1.5^(n+1) / (n+1)! which is less than .00001 only after 10 terms when it should be 9.