# Homework Help: (-1)^n/(n)! find the sum from n=0 to n=infinity

1. Sep 27, 2011

### chupe

1. The problem statement, all variables and given/known data

(-1)^n/(n)! find the sum from n=0 to n=infinity and do the same for (-1)^n/(2n)! Show all work

2. Relevant equations

3. The attempt at a solution

First answer is .367876. I just dont know how to expand out (2n)!. I know (n)! is expanded like: 1*1, 1*2, 1*2*3, 1*2*3*4...... and etc. However I don't know how the expanded version of (2n)! works.

2. Sep 27, 2011

### lineintegral1

Re: Series

You have likely derived Taylor Expansions for some common functions, like the exponential and trigonometric functions. Can you use these to evaluate your sum?

3. Sep 27, 2011

### SammyS

Staff Emeritus
Re: Series

It looks like (-1)n/(n)! should give 1/e = e-1 ≈0.36787944117144233

Write the first several terms for each series. Follow lineintegral1's suggestions

Also, (2n)! = 1*2*3*4* ... *(n-2*(n-1)*(n)*(n+1)*(n+2)* ... *(2n-2)*(2n-1)*(2n).

(2*0)! = 0! = 1

(2*1)! = 2! = 2

(2*2)! = 4! = 24

(2*3)! = 6! = 720

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Last edited: Sep 27, 2011
4. Sep 27, 2011

### chupe

Re: Series

Thank you so much!