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For $0< y< x$, natural number $n$ and any continuously differentiable function $f$: $$\sum_{y< n\leq x}f(n)=\int_y^x f(t)dt+\int_y^x \{t\} f'(t)dt-\{x\} f(x)+\{y\}f(y)$$
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Tue, 15 Jan 2019 07:36 GMT