Inspired by Yan Shee

Algebra Level 4

\[ \large \sum_{n = 1} ^\infty \dfrac{n^2 + n}{2 \times 10^n}\]

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

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