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 December 22nd, 2009, 12:54 AM #1 Newbie   Joined: Dec 2009 Posts: 1 Thanks: 0 Compare Let$(a_{n})$ be a sequence given by $a_{1}=1$ $a_{n+1}=\sqrt[]{a_{n}(a_{n}+1)(a_{n}+2)(a_{n}+3)+2}$ for every $n \in N*$ Compare the sum: $S=\frac{1}{a_{1}+2}+\frac{1}{a_{2}+2}+\frac{1}{a_{ 3}+2}+...+\frac{1}{a_{2009}+2}$ with $\frac{1}{2}$

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