Fractional power inequality

If $n$ is a positive integer and $x < 1$ , shew that $\frac{1 - x ^{n + 1}}{n + 1} < \frac{1 - x ^{n}}{n}$ .

~10 minProof · checked by AIInequalitiesSequences & series

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIX. Inequalities, Examples XIX.b, No. 8

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