Inspired by Yan Shee

Algebra Level 4

n=1n2+n2×10n \large \sum_{n = 1} ^\infty \dfrac{n^2 + n}{2 \times 10^n}

The value of the infinite series above can be expressed in the form ab\dfrac{a}{b}, where aa and bb are positive coprime integers. Find a+ba+b .

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