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maximum sum of sequences

Source: Mongolia 1999 Teachers secondary level P3

May 6, 2021
Sequencealgebrainequalities

Problem Statement

Let (an)n=1∞(a_n)^\infty_{n=1} be a non-decreasing sequence of natural numbers with a20=100a_{20}=100. A sequence (bn)(b_n) is defined by bm=min⁡{n∣an≥m}b_m=\min\{n|an\ge m\}. Find the maximum value of a1+a2+…+a20+b1+b2+…+b100a_1+a_2+\ldots+a_{20}+b_1+b_2+\ldots+b_{100} over all such sequences (an)(a_n).
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