Weird Recurrence, Weirder Sum

Algebra Level 2

Let a1=2,a_1 = 2, a2=3,a_2 = 3, a3=7,a_3 = 7, and an=1+a1×a2××an1a_n = 1 + a_1 \times a_2 \times \cdots \times a_{n-1} for n4.n\ge 4. Find n=11an.\displaystyle \sum_{n=1}^\infty \dfrac 1{a_n}.

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