# Doing series is fun!

Recall that $\large (1+x)^n = 1+ \frac{nx}{1!} + \frac{n(n-1)x^2}{2!} + \cdots$

for $$-1<x<1$$.

Then what is $\large 1 + \frac{1}{3} + \frac{1\cdot3}{3\cdot6} + \frac{1\cdot3\cdot5}{3\cdot6\cdot9} + \cdots ?$


Notation: $$!$$ is the factorial notation. For example, $$8! = 1\times2\times3\times\cdots\times8$$.

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