Can someone give me an example of a sequence such that $$a_{n}=\int_{1}^{n}f(x)dx$$ converges but $$\int_{1}^{∞}f(x)dx$$ diverges.
2026-04-04 00:12:00.1775261520
Sequence converges but Improper Integral diverges
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Consider $a_n = \int_1^n \cos(2\pi x)\,dx.$