Prove the Dirichlet Kernel: 1/2 + cos(θ) + cos(2θ) + cos(3θ) + ... + cos(Nθ) =...

Question

Question

Prove the Dirichlet Kernel:

1/2 + cos(θ) + cos(2θ) + cos(3θ) + ... + cos(Nθ) = sin[(N+1/2)θ] / 2sin(θ/2) for all θ ≠ 2πn

Answer 1

Answer #1

coso + cos20 +--+COSNO - Rel ciotė 287-. t ė N) =rel cel ) = Rel cosNot i sinno-1 1-coso ti sino = Re-2sin? No tiz sin No cos

Answer 2

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