# The Binomial Question!

Algebra Level 4

Let $$C_0,C_1,C_2....$$ , denote the binomial coefficients $$^nC_0,^nC_1,^nC_2...$$ so on.

It can be proved that,

$$(C_1-C_3+C_5-C_7+\cdots) = a^{\frac{n}{b}} \sin(\dfrac{n\pi}{c})$$.

Then find $$a+b+c$$.

Details and Assumption

• $$a,b,c$$ are positive integers.
• $$a$$ and $$b$$ have their minimum possible value.
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