MathDB

15

Part of 1982 IMO Shortlist

Problems(1)

Prove the inequality for all s

Source: IMO LongList 1982 - P19

9/10/2010
Show that 1−sa1−s≤(1+s)a−1 \frac{1 - s^a}{1 - s} \leq (1 + s)^{a-1} holds for every 1≠s>01 \neq s > 0 real and 0<a≤10 < a \leq 1 rational.
Inequalitycalculusgeometric progressionIMO ShortlistIMO Longlist