# Reckon you can solve this recursion?

Calculus Level 5

Consider a sequence $$(a_n)_{n=1}^\infty$$ with $$a_1 = 1, a_2 = 2$$. Let $$\displaystyle S_n = \sum_{j=1}^n a_n$$ such that it satisfy the recurrence relation $$a_n = n\times S_{n-1}$$ for $$n=3,4,5,\ldots$$.

Lastly, denote $$s$$ as the value of $$\displaystyle \sum_{n=1}^\infty \dfrac n{a_n}$$.

Find the last three digits of $$\left\lfloor 10^8 \times s \right\rfloor$$.

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