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Arithmetic Sequence

Source: 1999 National High School Mathematics League, Exam One, Problem 15

March 10, 2020

arithmetic sequence

Problem Statement

Given positive integer

n

and positive number

M

. For all arithmetic squence

a_1,a_2,\cdots,

that

a_1^2+a_{n+1}^2\leq M

, find the maximum value of

S=a_{n+1}+a_{n+2}+\cdots,a_{2n+1}