Let $K \leq 3$ an integer. Prove that $$\underset{i=0}{\overset{K}{\sum}}\frac{\left(-1\right)^{i}}{i!}\frac{\left(K-i-1\right)^{2}}{\left(K-i\right)!}=0.$$

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- May 21st 2014, 06:39 AMOmeroA strange way to write 0
Let $K \leq 3$ an integer. Prove that $$\underset{i=0}{\overset{K}{\sum}}\frac{\left(-1\right)^{i}}{i!}\frac{\left(K-i-1\right)^{2}}{\left(K-i\right)!}=0.$$

- May 21st 2014, 10:58 AMHallsofIvyRe: A strange way to write 0
You

**can't**prove it- it isn't true! Just calculate the K= 0 or K= 1 cases to see that . - May 21st 2014, 12:41 PMSlipEternalRe: A strange way to write 0
It is true if you reverse the inequality. If , it holds. Here is a rough outline for a proof:

For :

Edit: The crux of the proof involves trying to make each term resemble the binomial formula for for some power .