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For some positive integer \(n,\) 

\(\csc (2^3)^\circ + \csc (2^4)^\circ + \csc (2^5)^\circ + \dots + \csc (2^{2019})^\circ = \sec n^\circ.\)

Find the smallest possible \(n.\)

 May 17, 2023
 #1
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+1

Solved by computer:

 

for (n = 3..2019) {

   x = x + cscdeg(2^n);

}

 

output(x);

 

output = 1.002441898

 

This is equal to \(\sec 4^\circ\), so n = 4.

 May 17, 2023
 #2
avatar+214 
0

I'm glad you could give me this answer. Thanks!

Could someone show me a detailed way to solve this problem so I can use it elsewhere?

 May 18, 2023

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