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sum a_ib_i <= sum a_i B_i

Source: 1969 Swedish Mathematical Competition p3

March 21, 2021
algebrainequalities

Problem Statement

a1≤a2≤...≤ana_1 \le a_2 \le ... \le a_n is a sequence of reals b1,b2,b3,...,bnb_1, _b2, b_3,..., b_n is any rearrangement of the sequence B1≤B2≤...≤BnB_1 \le B_2 \le ...\le B_n. Show that ∑aibi≤∑aiBi\sum a_ib_i \le \sum a_i B_i.
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