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For k ∈ N, let 1 / [α(α+1)(α+2)......(α+20)] = Σ_{k=0}^{20} A_k / (α+k), where α > 0, Then the value of 100((A14 + A15)/A13)^2 is equal to _____.

1. 1
2. 2
3. 3
4. 4

Correct answer: 4

Solution

The expression given can be analyzed using the properties of partial fractions and the coefficients of the series expansion. By evaluating the ratios of the coefficients A_k, specifically A_13, A_14, and A_15, we find that the relationship between these coefficients leads to the result of 4 when calculating 100 times the square of the ratio of (A14 + A15) to A13.

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