Here is a known inequality: $$(1-x)^n\leq 1+\frac{nx}{2}\qquad \text{for} \, \frac 1n\leq x\leq 1 $$ I am wondering if there is a better upper bound than this? Thank you.
2026-04-11 11:14:40.1775906080
Sharpness of the upper bound $(1-x)^n \leq 1 + \frac{nx}{2}$
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