# Binomial Expansion

$(1+2x)^{50} = a_0 + a_1x + a_2 x^2 + \cdots + a_{50} x^{50}$

Let $$a_0 , a_1, \ldots , a_{50}$$ be constants such that equation above is an identity.

And let $$S = a_1+a_3 + \cdots +a_{49}$$. If $$S$$ can be expressed as $$\dfrac{3^n-1}{m}$$, where $$m$$ and $$n$$ are positive integers, find the value of $$m+n$$.

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