Strategic Minimalism

Calculus Level 5

The value of the infinite sum

$$\dfrac{1}{5} + \dfrac{1}{10} + \dfrac{3}{85} + \dfrac{1}{65} + \dfrac{5}{629} + \dfrac{3}{650} + \dfrac{7}{2405} + (\cdots)$$

can be written as $$\dfrac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers. Evaluate $$a+b$$.

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