MathDB
2014 Guts #26: Sum of Reciprocals of Sequence

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August 26, 2014

Problem Statement

For 1≤j≤20141\leq j\leq 2014, define bj=j2014∏i=1,i≠j2014(i2014−j2014)b_j=j^{2014}\prod_{i=1, i\neq j}^{2014}(i^{2014}-j^{2014}) where the product is over all i∈{1,…,2014}i\in\{1,\ldots,2014\} except i=ji=j. Evaluate 1b1+1b2+⋯+1b2014.\dfrac1{b_1}+\dfrac1{b_2}+\cdots+\dfrac1{b_{2014}}.
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