Factorial Series

Calculus Level 3

1!4!+2!5!+3!6!+4!7!+\large\dfrac{1!}{4!}+\dfrac{2!}{5!}+\dfrac{3!}{6!}+\dfrac{4!}{7!}+\cdots

If the value of the above series can be expressed to ab\dfrac{a}{b} when aa and bb are coprime positive integers. Find the value of a+ba+b.

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