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Let {an}\{a_{n}\}{an} be a sequence of real numbers satisfying {a0=1an+1=4+3an+an2−2for n≥0. \begin{cases} a_{0}=1 \\ a_{n+1}=\sqrt{4+3a_{n}+a_{n}^{2}}-2 & \text{for } n \ge 0. \end{cases} {a0=1an+1=4+3an+an2−2for n≥0. Let S=∑n=0∞an\displaystyle S=\sum_{n=0}^{\infty} a_{n}S=n=0∑∞an.
This problem is based on a recent Putnam contest problem.
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