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Prove or disprove: If the sequence In converges, then ∫ f(x) converges

The following function f is defined for all x \geq 1, and n is a positive integer. Prove or provide a counterexample to the following statement.

The convergence of the sequence \{ I_n \} implies the convergence of the integral

    \[ \int_1^{\infty} f(x) \, dx. \]


Incomplete.

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