Elementary inequalities proved by direct algebraic manipulation

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Problem 5.2 from Seber G.A., Lee A.J. "Linear Regression Analysis" [SeLe03]More problems in Chapter 5 "Confidence Intervals and Regions"

Prove that (1−α/k)k>1−α(k>1)(1-\alpha / k)^{k} > 1-\alpha \quad (k > 1).

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References

[SeLe03] Seber G.A., Lee A.J. Linear Regression Analysis. 2nd ed., John Wiley & Sons, 2003.