nu sin(kx) 2. Let pe R. Consider the series kep ka1 (a) Prove that the series converges absolutely uniformly on R for p

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Nu Sin Kx 2 Let Pe R Consider The Series Kep Ka1 A Prove That The Series Converges Absolutely Uniformly On R For P 1 (26.84 KiB) Viewed 25 times

nu sin(kx) 2. Let pe R. Consider the series kep ka1 (a) Prove that the series converges absolutely uniformly on R for p > 1. (b) Using the fact that sin(kx) sin (1) = } (cos((k – 1) ) - cos ((k + ) a)), show that for any meN sin("") sin ( m+1)=) Fm(x) = sin(kx) - COS (m. TT sin (6) kel sin(kx) (c) Let ne N. Define S = = ) Show that for any n e N * ki 1 S. () = e) - Hamad n+F.(2) + IF() (á x+1) 1 k+ kel