How to prove/disprove <munderover> &#x220F;<!-- ∏ --> <mrow class="MJX-TeXAtom-ORD">

Misael Matthews

Misael Matthews

Answered question

2022-06-14

How to prove/disprove k = 1 n cos ( k π n ) = ( 1 ) n + 1 2 2 n 1 for odd n?

Answer & Explanation

assumintdz

assumintdz

Beginner2022-06-15Added 22 answers

P ( z ) = k = 1 n ( z e 2 i k π / n ) = z n 1
k = 1 n cos ( k π / n ) = 2 n k = 1 n ( e i k π / n + e i k π / n ) = 2 n k = 1 n ( 1 + e 2 i k π / n ) = 2 n ( 1 ) n P ( 1 )

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