# Neither One nor Two but Three Geometric Series in One

Level pending

Let $$\frac{1}{7}$$ + $$\frac{3}{7^2}$$ + $$\frac{6}{7^3}$$ + $$\frac{10}{7^4}$$ + $$\frac{15}{7^5}$$ + $$...$$ = $$\frac{a}{b}$$ , with $$a$$ and $$b$$ are coprime, what is $$a + b$$ ?

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