Justify: "The infinite series sum_{n=1}^infinity sin(nx)/sqrt(n) converges for x ϵ R, but it does not correspond to the Fourier series of an integrable function on [-pi, pi]."
Added by Cristina V.
Step 1
First, we need to show that the infinite series converges for x ϵ R. To do this, we can use the Dirichlet's test for convergence. Dirichlet's test states that if we have two sequences a_n and b_n such that: a) a_n is a sequence of real numbers such that the Show more…
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