## MMM #35: Fibonacci Fun

Blinkdagger has announced the winner and the solution for MMM #34. Now, it's time for MMM #35.

I want to thank Blinkdagger for running 17 contests over the last year and a half. Quan and Daniel have done an excellent job of creating problems and engaging you with fun problem descriptions and great graphics. I'll miss their participation.

Here's Monday Math Madness #35:

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.

Here are the rules for the contest:

1. Email your answers with solutions to mondaymathmadness at gmail dot com.

2. Only one entry per person.

3. Each person may only win one prize per 12 month period. But, do submit your solutions even if you are not eligible.

4. Your answer must be explained. You must show your work! Wild About Math! and Blinkdagger will be the final judges on whether an answer was properly explained or not.

5. The deadline to submit answers is Tuesday, June 30, 12:01AM, Pacific Time. (That’s Tuesday morning, not Tuesday night.) Do a Google search for “time California” to know what the current Pacific Time is.)

6. The winner will be chosen randomly from all timely well-explained and correct submissions, using a random number generator.

7. The winner will be announced Friday, June 3, 2009.

8. The winner (or winners) will receive a Rubik’s Revolution or a $10 gift certificate to Amazon.com or $10 USD via PayPal. For those of you who don’t want a prize I’ll donate $10 to your favorite charity.

9. Comments for this post should only be used to clarify the problem. Please do not discuss ANY potential solutions.

10. I may post names and website/blog links for people submitting timely correct well-explained solutions. I’m more likely to post your name if your solution is unique.

AlecJune 23rd, 2009 - 19:22

Just FYI, the Fibonacci Numbers are normally defined as F_0 = 0, F_1 = 1, and so on (one position off from where you put it).