Question

find the sum of the series 1 - e + e^2/2! - e^3/3! + e^4/4! - ...

Answer 1

\[\sum_{0}^{?\infty}(-e)^n/(n!)\]

Answer 2

the top shouldnt have a question mark but that should look like something u can solve

Answer 3

thanks

Answer 4

I can write the sum out for you:
\[\sum_{k=0}^{\infty}\frac{(-1)^n x^n}{n!}\]
That looks close to e^x. But e^x is:
\[\sum_{k=0}^{\infty}\frac{x^n}{n!}\]
So, pull the n power out:
\[\sum_{k=0}^{\infty}\frac{(-x)^n}{n!}=e^{-x}\]

Answer 5

Of course, for your case it would be e^(-e)

Answer 6

Sorry, I didn't realize someone answered already :P

Answer 7

np it helps with the steps

Answer 8

n yours explained more anyway

Answer 9

Thank you :D