Solution of Assignment 5

    7 First, we show n≥2 sin(nx) log(n) − − − * converges for every x. Since, we see that (a) fixed x, for any m ≤ 2, m n=2 sin(nx) is bounded. (see no.8 in assignment 2) (b) 1 log(n) decreases monotonically to zero. Hence, by Dirichlet 's test (see no.7 in assignment 2), n≥2 sin(nx) log(n) converges for all x. Then, we show that it is not a fourier series of a… (More)