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219

Part of 1952 Moscow Mathematical Olympiad

Problems(1)

MMO 219 Moscow MO 1952 (1-x)^n + (1 + x)^n < 2^n if n>= 2, |x| < 1

Source:

8/8/2019
Prove that (1−x)n+(1+x)n<2n(1 - x)^n + (1 + x)^n < 2^n for an integer n≥2n \ge 2 and ∣x∣<1|x| < 1.
inequalitiesalgebra