Series/binomial/multinomial theorum

[roadrunner]

Homework Statement

for any positive interget n determine

a) SUM(from i=0 to n) of

(-1)^i
i!(n-i)!

b) SUM (from i=0 to n) of

1
i!(n-1)!

Homework Equations

The Attempt at a Solution

a) well i didnt realyl know how to start. i found that with
n=1 then it becomes 1+1
n=2 .5+1+.5
n=3 1/3! + .5 +.5 +1/3!
n=4 1/4! +1/3! +.25 +1/3! +1/4!
n=4 1/5! +1/4! +.083333 +.083333 +1/4! +1/5!

so i guess what i need is how do i get the middle term?
or am i going about it wrong?

for b) i know the sum is always 0, because ichecked it on my calculator. but i don't know hwo to prive that

 

[Avodyne]

Do you know what the binomial expansion of (1+x)ⁿ is?

 

[roadrunner]

i acctulay think i got it
a) 2^n/n!

 

[Avodyne]

Yes. Do the binomial expansion of (1+x)ⁿ, and the set x=1 or -1 to get the two versions of your problem.

 

[roadrunner]

so is the 2^n/n! right?
i get the same answer doing that as i do doing it long form (calculator)

(mind helping on my other post ? :P)