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Example 1.7 For any 0 <0<r and any positive integer n show the inequality sin ne sin 20 2 sin + for 00< 2π, + + n=1 This was conjectured by Fejér and proved by Jackson (1911) and by Gron- wall (1912) independently. Landau (1934) gave a shorter (maybe the shortest) elegant proof. See also PROBLEM 5.9. Note that sin ne n n = > 0. π-0 2
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