Yet another question 4 - Corrected

Algebra Level 5

Let ak=(k2+1)k!a_k = (k^2 +1) k! and bn=k=1nakb_n = \displaystyle \sum_{k=1}^{n} a_k.

a100b100\dfrac{a_{100}}{b_{100}} can be represented as AB\dfrac AB for positive coprime integers AA and BB.

Find BAB-A.


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