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$$1+\frac{1}{3}+\frac{1\cdot 3}{3\cdot 6}+\frac{1\cdot 3\cdot 5}{3\cdot 6\cdot 9}+\frac{1\cdot 3\cdot 5\cdot 7}{3\cdot 6\cdot 9\cdot 12}+\dots$$

How do I proceed on evaluating this sum.

jimjim
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saurabh742
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    Make the connection with the Taylor development of $1/\sqrt{1-x}$. –  Jan 25 '17 at 07:53
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    see http://math.stackexchange.com/questions/1692678/prove-that-1-frac13-frac1-cdot-33-cdot-6-frac1-cdot-3-cdot-53-cdo. I can't write it in comment. So I'm posting in answer. – Arun Jan 25 '17 at 08:01

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