Recent content by tony700

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    MHB How would I prove this by induction?

    How would I prove this by induction? $$\sum_{k=0}^n\frac{n!}{n^kk!(n-k)!}=\frac{(n+1)^n}{n^n}$$
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    MHB Stuck on the sides of a triangle problem

    I have figured out the triangle's height and base, but I need to figure out sides a and b. I have tried Pythagorean theorem and similar triangle ratios, but it is not working out. Please help. See picture below. Thank you.
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    Proving an equality using induction proof not working

    Homework Statement I work out the problem completely and it does not equal out. Having problems with two variable induction proofs (n and k) in this problem. Below is as far as I got, jpeg below Homework EquationsThe Attempt at a Solution
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    Graduate Pythagorean theorem based on cross product.

    Yes, you pointed out a major flaw in this one...I forgot to put the other points in space to delineate it as a right triangle...How does this look? http://www.scribd.com/doc/203932954/3-d-Cross-Product-Proof-Math-is-Art-Pythagorean-Theorem-Proof
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    Graduate Pythagorean theorem based on cross product.

    I was developing a pythagorean theorem proof based on the cross product of two vectors..Below is my final solution...My problem is I had to get around using the distance/magnitude formula because that is using the pythagorean theorem to prove the pythagorean theorem. But after searching, it may...