Does cover up rule help?

Algebra Level 4

The partial fraction of 1(x+1)(x+2)(x+3)(x+100) \dfrac1{(x+1)(x+2)(x+3)\cdots(x+100) } can be written as j=1100ajx+j \displaystyle \sum_{j=1}^{100} \dfrac{a_j}{x+j} , where a1,a2,,a100a_1,a_2,\ldots,a_{100} are constants. What is the value of a1+a2++a100a_1 + a_2 + \cdots + a_{100} ?

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