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Prove the inequality for all s

Source: IMO LongList 1982 - P19

September 10, 2010
Inequalitycalculusgeometric progressionIMO ShortlistIMO Longlist

Problem Statement

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.
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