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For k in N ,let (1)/( alpha (alpha +1) (...

For `k in N ,`let `(1)/( alpha (alpha +1) (alpha +2) .....(alpha + 20)) = sum _( k =0) ^( 20) (A _(k))/( alpha + k ), ` where `a gt 0.` Then the value of `1000 ((A _(14) + A _(15) )/( A _(13))) ` is equal to _________.

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