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## Limit

Real & Complex Analysis, Calculus & Multivariate Calculus, Functional Analysis,
Tolaso J Kos
Let $f(x)$ be a striclty decreasing function of a zero limit. Prove that the limit of the integral of the function minus the sum of the function (the limit is to be taken as $n \rightarrow +\infty$) exists and equals at most $f(1)$.