# Summed Fraction Factorials

Algebra Level 5

If

$$\frac {3}{1! + 2! + 3!} + \frac {4}{2! + 3! + 4!} + \frac {5}{3! + 4! + 5!} + \ldots + \frac {2001}{1999!+ 2000! + 2001!} = \frac {a}{b} - \frac {c}{d!}$$,

what is the digit sum of $$(abcd)^{(abc)^{(ab)^a}}$$? Assume that $$a$$and $$b$$; and $$c$$ and $$d!$$ are co-prime.

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