# What is Putnam exam/competition?

Just heard of Putnam competition. There is not a lot of info about it on the net. Could you tell me a little about it? What is its purpose? What kind of math levels does it test? Also, I found a sample question from the exam. Anybody have an idea on how to go about it. You don't have to give the whole solution. Just the first couple steps. Thanks.

Consider the power series expansion $$\dfrac{1}{1-2x-x^2}=\sum_{n=0}^{\infty}a_nx^n.$$Prove that, for each integer $n\ge0$, there is an integer $m$ such that $$a_n^2+a_{n+1}^2=a_m.$$

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In short, it is an incredibly difficult 6 hour exam that will test nearly all of your mathematical ability. The median score is 0 nationwide, so that should be an indicator. –  Jeremy Apr 12 '13 at 4:08
You may want to copy the Putnam question into your question. It changes daily... –  Potato Apr 12 '13 at 4:12
–  mixedmath Apr 12 '13 at 4:30
–  raindrop May 25 '13 at 3:46
Regarding the problem you posted, my first guess would be to try making use of the "sum of an infinite geometric series" formula after expanding the left side using partial fractions. I bet this will get you somewhere useful if this is one of the first two morning problems or one of the first two afternoon problems. But if it's not one of these four problems, I suspect a bit more creativity will be needed! –  Dave L. Renfro Dec 13 '13 at 15:00