Does cover up rule help?

Algebra Level 3

The partial fraction of \( \dfrac1{(x+1)(x+2)(x+3)\cdots(x+100) } \) can be written as \( \displaystyle \sum_{j=1}^{100} \dfrac{a_j}{x+j} \), where \(a_1,a_2,\ldots,a_{100} \) are constants. What is the value of \(a_1 + a_2 + \cdots + a_{100} \)?

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