Here's a calc 2 question that has been irritating me for a while: Use the maclaurin expansion for e^x to show that e = (reimannsumof) from 0 to infiniti of 1/n!.... what theorems about series are involved in justifying this claim?
Also, should I just memorize these maclaurin sums... ?

Question

Here's a calc 2 question that has been irritating me for a while: Use the maclaurin expansion for e^x to show that e = (reimannsumof) from 0 to infiniti of 1/n!.... what theorems about series are involved in justifying this claim? 
Also, should I just memorize these maclaurin sums... ?

amistre64 · Answer

$$e^x = \sum_{n=0}^{+ \infty} \frac{x^n}{n!}$$

amistre64 · Answer

x=0 of e^x;  f(x) = e^x;  f'(x) = e^x; f''(x)=e^x..etc

amistre64 · Answer

e^0 = 1

amistre64 · Answer

$$e^x=1+\frac{x}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}+\frac{x^5}{5!}+...\frac{x^n}{n!}$$

anonymous · Answer

Thank you amistre64! I'm now a little confused on the second question... the theorems that justify this...