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

Source: 1967 Swedish Mathematical Competition p5

March 21, 2021
algebrainequalities

Problem Statement

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.
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