The Binomial Question!

Algebra Level 4

Let C0,C1,C2....C_0,C_1,C_2.... , denote the binomial coefficients nC0,nC1,nC2...^nC_0,^nC_1,^nC_2... so on.

It can be proved that,

(C1C3+C5C7+)=anbsin(nπc)(C_1-C_3+C_5-C_7+\cdots) = a^{\frac{n}{b}} \sin(\dfrac{n\pi}{c}).

Then find a+b+ca+b+c.

Details and Assumption

  • a,b,ca,b,c are positive integers.
  • aa and bb have their minimum possible value.
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