xuying1209
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if n is an odd, cosπ/n+cos3π/n+cos5π/n+...+cos(2n-1)π/n is equal to what?
And how can I prove it??
And how can I prove it??
Sum of cosines with odd multiples of π/n when n is odd
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For n= 1, cos(pi/1)= -1.
For n> 1, n odd, essentially you are adding the real parts of the 2nth roots of unity. Since those roots are symmetric about the imaginary axis, the sum is 0.
For n> 1, n odd, essentially you are adding the real parts of the 2nth roots of unity. Since those roots are symmetric about the imaginary axis, the sum is 0.
tehno
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Ahh that it was... almost racked my brains out 'cause "π" I read as n ( not [itex]\pi[/itex]) ...
robert Ihnot
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I am not sure what is being asked. Is this [tex]\sum cos(n_i)/n_i, or \sum cos(pi*n_i/n_i), or what?[/tex]
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Science Advisor
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I interpreted as sum of [itex]cos(i\pi/n)[/tex] for i= 1 to n-1.[/itex]