Define $b_n = \int_0^{\pi} \cos (nx).\sqrt{x} ~ dx $.
Does the following series converge? $$ F(x) = \sum_{n=1}^{\infty} b_n \cos(nx) $$
Define $b_n = \int_0^{\pi} \cos (nx).\sqrt{x} ~ dx $.
Does the following series converge? $$ F(x) = \sum_{n=1}^{\infty} b_n \cos(nx) $$
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