MathDB

5

Part of 1967 Swedish Mathematical Competition

Problems(1)

a_n \ge C n when C > 0, a_n^2 >= a_1 + a_2 +... + a_{n-1}

Source: 1967 Swedish Mathematical Competition p5

3/21/2021
a1,a2,a3,...a_1, a_2, a_3, ... are positive reals such that an2≥a1+a2+...+an−1a_n^2 \ge a_1 + a_2 +... + a_{n-1}. Show that for some C>0C > 0 we have an≥Cna_n \ge C n for all nn.
algebrainequalities