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# (M) ∑(k=1,n)[C(n,k)*sin(kx)] = _________.?

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- IndicaLv 73 years agoFavorite Answer
∑(k=0,n) C(n,k)exp(kix) = (1+exp(ix))ⁿ = (exp(ix/2))ⁿ(exp(ix/2)+exp(−ix/2))ⁿ = exp(nix/2)(2cos(x/2))ⁿ

Equate imaginary parts for ∑(k=1,n)C(n,k)sin(kx) = 2ⁿsin(nx/2)cosⁿ(x/2)

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