MathDB
Question 4

Source: Iran TST 2006

April 18, 2006
inequalitiesinductionfunctiontriangle inequalityinequalities proposed

Problem Statement

Let x1,x2,…,xnx_1,x_2,\ldots,x_n be real numbers. Prove that ∑i,j=1n∣xi+xj∣≥n∑i=1n∣xi∣ \sum_{i,j=1}^n |x_i+x_j|\geq n\sum_{i=1}^n |x_i|
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