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Condition for a series to converge

Source: 2019 South Korea USMC P7

August 13, 2020
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Problem Statement

For a real number aa and an integer n(≥2)n(\geq 2), define Sn(a)=na∑k=1n−11k2019(n−k)2019S_n (a) = n^a \sum_{k=1}^{n-1} \frac{1}{k^{2019} (n-k)^{2019}} Find every value of aa s.t. sequence {Sn(a)}n≥2\{S_n(a)\}_{n\geq 2} converges to a positive real.
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