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I want to solve the inequality but I can't type it in Mathematica and always get an error. It's too complicated for me.

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Please help me to solve it.

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  • $\begingroup$ @Feyre I have tried many structures to write it but I'm not able to write it $\endgroup$
    – S.H.W
    Jan 19 '17 at 11:29
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Make a function f[n] returning True if the inequality holds, and False if not:

f[n_] := n - 1 + (n - 1)/4 Sum[Csc[(i - 2) Pi/(n - 1)], {i, 3, n}] < 
  n/4 Sum[Csc[(i - 1) Pi/n], {i, 2, n}]

E.g. f[5] returns False.

n = 3;
While[! f[n], n++]
n

12

i.e. f[11] === False, but f[12] === True.

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  • $\begingroup$ Fantastic! Thank you $\endgroup$
    – S.H.W
    Jan 19 '17 at 11:48

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