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\int \limits_0^1 1/(1+x)^n dx > 1- 1/n

Source: 1972 Swedish Mathematical Competition p5

March 26, 2021
integrationalgebraanalysis

Problem Statement

Show that ∫011(1+x)ndx>1−1n \int\limits_0^1 \frac{1}{(1+x)^n} dx > 1-\frac{1}{n} for all positive integers nn.
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