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Omni-MATH / For 1≤j≤2014, define b_(j)=j²⁰¹⁴∏_(i=1,i≠j)²⁰¹⁴(i²⁰¹⁴−j²⁰¹⁴) where the product is over all i∈{1,…,2014} except i=j. Evaluate (1)/(b₁)+(1)/(b₂)+⋯+(1)/(b₂₀₁₄).

Problem

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problem

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\frac{1}{b_{1}}+\frac{1}{b_{2}}+\cdots+\frac{1}{b_{2014}}.
Plain-text mathematical notation (without MathML)
For 1≤j≤2014, define b_(j)=j²⁰¹⁴∏_(i=1,i≠j)²⁰¹⁴(i²⁰¹⁴−j²⁰¹⁴) where the product is over all i∈{1,…,2014} except i=j. Evaluate (1)/(b₁)+(1)/(b₂)+⋯+(1)/(b₂₀₁₄).
Original LaTeX notation
For $1 \leq j \leq 2014$, define $b_{j}=j^{2014} \prod_{i=1, i \neq j}^{2014}(i^{2014}-j^{2014})$ where the product is over all $i \in\{1, \ldots, 2014\}$ except $i=j$. Evaluate $\frac{1}{b_{1}}+\frac{1}{b_{2}}+\cdots+\frac{1}{b_{2014}}$.

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Source and history

task_id
cb09aca1-0b56-5246-b954-4cdc6ad7544c
task_key
test--cb09aca1-0b56-5246-b954-4cdc6ad7544c
task_revision_id
1
config / split
/ test

Official source

initial import