# Yet another question 4 - Corrected

Algebra Level 5

Let $$a_k = (k^2 +1) k!$$ and $$b_n = \displaystyle \sum_{k=1}^{n} a_k$$.

$$\dfrac{a_{100}}{b_{100}}$$ can be represented as $$\dfrac AB$$ for positive coprime integers $$A$$ and $$B$$.

Find $$B-A$$.

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