Factorial!

If the expression \(\frac{3}{1!+2!+3!}\) + \(\frac{4}{2!+3!+4!}\) + ...... + \(\frac{2001}{1999!+2000!+2001!}\)

Can be written as \(\frac{1}{a!}\) - \(\frac{1}{b!}\), Find a+b.

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