Question

Someone please help me use infinite series to compute e^.4

Answer 1

when you say 'e', do you mean euler's number e? like 2.7?

Answer 2

I don't know it looks like\[e ^{.4}\]

Answer 3

Not quite @DemolisionWolf

Answer 4

Umm I don't know i have never seem it like that but when i do it on my calculator it's the one above the natural log (ln)

Answer 5

\[e^x=\sum_{n=0}^{\infty}\frac{ x^n }{ n! }\]

Answer 6

@Kainui teach me, i'm a noob

Answer 7

@DemolisionWolf
http://www.wolframalpha.com/input/?i=power+series+of+e%5Ex

Answer 8

You're taking each individual term to the power, when in actuality you've turned something that looks like:

(a+b+c)^x and saying it equals something like a^x+b^x+c^x which is clearly wrong.

Answer 9

i get ya

Answer 10

So this is really an incomplete question. To what degree of accuracy do you need to calculate e^.4? Because you can just keep adding terms until you get to whatever decimal place of accuracy you need.

Answer 11

i need to have 4 numbers after the decimal

Answer 12

So do you know how to read a power series?

Answer 13

not really because thats not exactly how we were learning it

Answer 14

Oh can you sort of explain how you're learning it then? I want to make sure you understand what I'm talking about so that it actually helps you!

Answer 15

The formula I guess that my teacher gave us is \[e^x=1+x+\left(\begin{matrix}x^2 \\2 \end{matrix}\right)\]