A Sequence Defined by Factorial Sums

Difficulty: Hard · Topics: Algebra, Sequences, Limits

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The sequence \a n\ satisfies the following:

Σ k=1^n(a k)/((k-1)!)=(3)/((n+2)!), n=1,2,3,…

Evaluate lim n→∞≤ft(a 1+n^2a n ).