Find the sum of the series(adsbygoogle = window.adsbygoogle || []).push({});

[tex] 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{6} + \frac{1}{8} + \frac{1}{9} + \frac{1}{12} + \dotsb [/tex]

where the terms are the reciprocals of the positive integers whose only prime factors are 2s and 3s.

Well, here is my guess:

[tex] 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{6} + \frac{1}{8} + \frac{1}{9} + \frac{1}{12} + \dotsb = 1 + \sum _{n=1 } ^{\infty} \left( \frac{1}{2} \right) ^n + \sum _{n=1 } ^{\infty} \left( \frac{1}{3} \right) ^n + \sum _{n=1 } ^{\infty} \left( \frac{1}{2\cdot 3} \right) ^n + \mbox{ ? } = \sum \frac{1}{2^x \cdot 3 ^y} [/tex]

As you can readily observe, I'm really stuck. Maybe someone could give me a tip. Any help is highly appreciated.

Thanks

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# Homework Help: Series pattern

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