Zeta product.

Calculus Level 3

Find the value of

∏ n = 2 ∞ ⌊ ζ ( n ) ⌋ . \prod _{ n=2 }^{ \infty }{ \left\lfloor \zeta (n) \right\rfloor } .


The answer is 1.

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Shivamani Patil by shivamani patil , 21, India

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3 solutions

Steven Zheng
Oct 1, 2014

For integers n > 1 n>1 , we have 1 < ζ ( n ) < 2 1<\zeta(n) <2 . Therefore we have an infinite product of 1 for this question.

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Michael Mendrin
Aug 18, 2014

The zeta function is barely over 1 for most n

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ethan W
Jan 7, 2015

ListLinePlot[FoldList[Times, 1, Table[Floor[Zeta[n]], {n, 2, 162}]]]

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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