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Σ1/x_i^n from i=1 to i=k \ge k^{n+1} when Σx_i=1

Source: Vietnamese MO (VMO) 1976 P6

August 20, 2018
algebrainequalitiesInequality

Problem Statement

Show that 1x1n+1x2n+...+1xkn≥kn+1\frac{1}{x_1^n} + \frac{1}{x_2^n} +...+ \frac{1}{x_k^n} \ge k^{n+1} for positive real numbers xix_i with sum 11.
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