# Solving inequality in Mathematica involving summation [closed]

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.

## closed as off-topic by Feyre, corey979, MarcoB, bbgodfrey, SaschaJan 20 '17 at 6:53

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• @Feyre I have tried many structures to write it but I'm not able to write it – S.H.W Jan 19 '17 at 11:29

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.

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