VMO 1989 Problem 1
Show that the absolute value of sin(kx) /N + sin(kx + x) /(N+1) + sin(kx + 2x) /(N+2) + ... + sin(kx + nx) /(N+n) does not exceed the smaller of (n+1) |x| and 1/(N sin(x/2) ), where N is a positive integer and k is real and satisfies 0 ≤ k ≤ N.
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