It Telescopes?

Calculus Level 3

Let {an}\{a_{n}\} be a sequence of real numbers satisfying {a0=1an+1=4+3an+an22for n0. \begin{cases} a_{0}=1 \\ a_{n+1}=\sqrt{4+3a_{n}+a_{n}^{2}}-2 & \text{for } n \ge 0. \end{cases} Let S=n=0an\displaystyle S=\sum_{n=0}^{\infty} a_{n}.

  • If SS converges, submit your answer as 100S\big\lfloor 100S \big\rfloor.
  • If SS diverges, submit your answer as 1-1.

This problem is based on a recent Putnam contest problem.


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