# Math Help - Taylor's theorem and e

1. ## Taylor's theorem and e

Explain why Taylor's Theorem guarantees that we can use a Taylor polynomial to estimate the value of e to any degree fesired
the taylor series for e is
$1/0! + 1/1! * x + 1/2! * x^2 + 1/3! * x^3 + ... 1/n! * x^n$

I really have no clue on this one. We never talked about e in class.

2. Originally Posted by diroga
the taylor series for e is
$1/0! + 1/1! * x + 1/2! * x^2 + 1/3! * x^3 + ... +1/n! * x^n$

I really have no clue on this one. We never talked about e in class.
You don't need to have, all you need is that you have done Taylor's theorem and know at least one form of the remainder for a truncated Taylor series and the general term of the series in question.

Now what you have to do is show that for fixed x the remainder can be made as small as you like by truncating sufficiently far to the right in the series.

CB