Wild About Math! Making Math fun and accessible

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?