Wild About Math!

Now that the MMM #35 deadline has passed …

MMM #35 turned out to be harder than I thought judging by the small number of submissions I received.

I’ll be giving away four prizes on Friday - two to the early submitters, one to .mau. for consistently submitting entries to the contest for a really long time, and one to a randomly selected person with a correct submission.

I’ll discuss some of the solutions on Friday but, for now, check out these pictures I made. I came up with this problem by playing with the Fibonacci series and arranging rectangles.

Here is the problem description:

Let F(0)=1, F(1)=1, and F(n)=F(n-2)+F(n-1). This is the familiar Fibonacci series.

Simplify F(0)xF(1) + F(1)xF(2) + F(2)xF(3) + F(3)xF(4) + … + F(n-1)xF(n) + F(n)xF(n+1)

Show your work.

Can you see how these pictures help one to see why the sum is what it is? Do you see why there are two different pictures?

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Can you sum this?

Hi,

I’ve been playing with this series:

S_n = 1×2² + 2×3² + 3×4² + … + nx(n+1)²

I’ve come up with a formula for determining S_n but I derived the formula in a fairly roundabout way.

I’m interested to know if someone has an elegant way to derive the formula.

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MMM #35: Is it too hard?

I’ve only gotten two solutions to the “Fibonacci Fun” problem I proposed. Is everyone on vacation and not thinking about Math, do people find the problem boring or is it too hard? I don’t think it’s one of my harder problems. I want to state that I approached the problem in a different way than each of the people who provided solutions. So, there are at least three ways to approach the problem.

If you don’t know how to approach it I suggest looking for a pattern in the sum as you add more terms.

Come on, give it a try! You could win $10.

This time around, since I’ve given you guys a hint, I’ll give three prizes - one each to the two people who have solved it already and one to a randomly other person with a correct solution.

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