Question 76
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
$$
\frac{1}{b_{1}} + \frac{1}{b_{2}} + \cdots + \frac{1}{b_{2014}}
$$
$$
b_{j} = j^{2014} \prod_{i=1, i \neq j}^{2014} (i^{2014} - j^{2014})
$$
where the product is over all $i \in \{1, \ldots, 2014\}$ except $i = j$. Evaluate
$$
\frac{1}{b_{1}} + \frac{1}{b_{2}} + \cdots + \frac{1}{b_{2014}}
$$