Another Factorial Summation! (CMI 2010)

Algebra Level 3

\[ \dfrac2{0! +1!+2!} + \dfrac3{1!+2!+3!} + \cdots+ \dfrac{100}{98!+99!+100!} \]

If the value of the expression above is equal to \(x\), evaluate \(x + \dfrac1{100!} \).

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