Infinite Sums

Calculus Level 3

If 19+118+130+145+163+=mn\dfrac{1}{9}+\dfrac{1}{18}+\dfrac{1}{30}+\dfrac{1}{45}+\dfrac{1}{63}+ \cdots =\dfrac{m}{n}, where mm and nn are coprime positive integers, then find m+nm+n.

This problem is a part of the sets Advanced is basic and Summing Sums.

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