# Homework Help: Sum with factorial

1. Jul 29, 2011

### dystplan

1. The problem statement, all variables and given/known data
$\sum_{n=0}^{100} 1/n!(100-n)!$

3. The attempt at a solution
Other then obvious attempts to make sense of the equation's incremental and decrements divisor, I can't figure out where to start with this question. Some assistance would be greatly appreciated.

2. Jul 29, 2011

### Dick

It looks like it's closely related to the sum of binomial coefficients. What's the sum of C(100,n) for n from 0 to 100? Is that enough of a hint?

3. Jul 29, 2011

### dystplan

C(100,n) being = 100!/n!(100-n)! ? hmmm, unfortunately I don't see where that's going =/

Man this one is throwing me for a loop, only question I haven't managed and due tomorrow.

4. Jul 29, 2011

### Dick

Yes, that's C(100,n). There is a simple formula for the sum of the binomial coefficients. It's related to the value of (1+1)^100. Don't know it? Expand (1+1)^100 using the binomial theorem.

5. Jul 29, 2011

### dystplan

well; thanks. But I'm still just totally lost. (1+1)^100 is a massive equation when expanded.

6. Jul 29, 2011

### dystplan

Unless... x/y = 0 or 1 in the binomial theorem? That would make it easy.

Makes it = 1/100! ?

7. Jul 29, 2011

### Dick

Oh come on, (1+1)^100=2^100. That's an easy enough number to write down. Now what does that have to do with the sum of the binomial coefficients C(100,n)?? C(100,0)+C(100,1)+...+C(100,100). I'm not asking you to evaluate each one. Just think about it.

8. Jul 29, 2011

### dystplan

wait;

2^100/100!

9. Jul 29, 2011

### dystplan

wait;

2^100/100!

10. Jul 29, 2011

### Dick

You aren't just guessing, I hope.