Show that \[ \frac{1 - s^a}{1 - s} \leq (1 + s)^{a-1}\] holds for every $1 \neq s > 0$ real and $0 < a \leq 1$ rational.
Problem
Source: IMO LongList 1982 - P19
Tags: Inequality, calculus, geometric progression, IMO Shortlist, IMO Longlist
Source: IMO LongList 1982 - P19
Tags: Inequality, calculus, geometric progression, IMO Shortlist, IMO Longlist
Show that \[ \frac{1 - s^a}{1 - s} \leq (1 + s)^{a-1}\] holds for every $1 \neq s > 0$ real and $0 < a \leq 1$ rational.