Is there a way to find the exact

Leia Sullivan

Leia Sullivan

Answered question

2022-04-15

Is there a way to find the exact value of the product
P=n=11007sin(nπ2015)

Answer & Explanation

WigwrannyErarmbmk

WigwrannyErarmbmk

Beginner2022-04-16Added 13 answers

By symmetry, your product is just:
P=n=12014sinnπ2015=122014n=12014(exp(2π2015)1)
where the innermost product is the product of the roots of the polynomial:
(x+1)20151x
Hence, by Vieta's theorem:
P=201522014=201521007

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