Series/binomial/multinomial theorum

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Homework Help Overview

The discussion revolves around evaluating sums involving factorials, specifically related to the binomial and multinomial theorems. The original poster presents two summation problems that involve alternating signs and factorial expressions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to evaluate the sums by substituting small values for n and observing patterns. They express uncertainty about how to derive the middle term in their calculations. Another participant inquires about the binomial expansion, suggesting it may be relevant to the problem. Some participants discuss the potential result of the first sum and its relation to the binomial expansion.

Discussion Status

Participants are exploring different interpretations of the summation problems. Some guidance has been offered regarding the binomial expansion, and there is an ongoing dialogue about the correctness of the proposed solutions. However, there is no explicit consensus on the final answers or methods.

Contextual Notes

The original poster mentions checking their results with a calculator, indicating a desire for verification of their findings. There is also a request for assistance on a related post, suggesting interconnectedness in the problems being discussed.

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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
 
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Do you know what the binomial expansion of (1+x)n is?
 
i acctulay think i got it
a) 2^n/n!
 
Yes. Do the binomial expansion of (1+x)n, and the set x=1 or -1 to get the two versions of your problem.
 
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)
 

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