<s>[INST] How to find $1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{6} + \frac{1}{8} + \frac{1}{9} + \frac{1}{12}+\cdots$? Find the sum of series $$1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{6} + \frac{1}{8} + \frac{1}{9} + \frac{1}{12}+\cdots,$$ where the terms are the reciprocals of positive integers whose only prime factors are two's and three's:
 [/INST] Hint: factor
$$\sum_{i=0}^\infty \sum_{j=0}^\infty \frac{1}{2^i 3^j}$$
as the product of a sum over $i$ and a sum over $j$.
</s>