It's time for Monday Math Madness #7. I love infinite series and I found today's infinite series problem on the web. This is one of the most interesting of these kinds of problems I have run into. It's challenging but not brutally difficult, so give it a try. I won't reveal the source until the contest ends because the answer is posted with the problem.
Thanks to the sponsors for this contest, I have one $25 gift certificate left for the Art of Problem Solving. I also have a couple of Rubik's Revolutions, courtesy of Techno Source. Depending on how many correct solutions I get I may give away two prizes.
Here's the problem:
What is the sum of this infinite series?
The subscripted F terms refer to the familiar Fibonacci series where F0=1, F1=1, and Fn=Fn-2+Fn-1 for n > 1.
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.
3. 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.
4. The deadline to submit answers is Tuesday, June 3, 2008 12:01AM, Pacific Time. (That’s Tuesday morning, not Tuesday night.)
5. The winner will be chosen randomly from all timely well-explained and correct submissions, using a random number generator.
6. The winner will be announced Friday, June 6, 2008.
7. The winner (or winners) will receive a $25 gift certificate, graciously donated by the Art of Problem Solving. I may give other prizes if there are many entries.
8. Comments for this post should only be used to clarify the problem. Please do not discuss ANY potential solutions.
9. I will post names and website/blog links for people submitting timely correct well-explained solutions UNLESS I get too many entries, in which case I'll post a subset of these.