A Pinned Sum of Squares

★ 7/10Arithmetic Progression sequences Cauchy-Schwarz inequality

Problem

Let $S_n$ be the sum of the first $n$ terms of an arithmetic sequence $\{a_n\}$ whose terms are all nonzero reals. For a given integer $n > 1$ and positive number $M$ , the sequence satisfies

a_1^2 + a_{n+1}^2 = M.

Find the maximum possible value of $S_n$ .

Answer

Solution

Difficulty	7/10
Topics	Arithmetic Progression, sequences, Cauchy-Schwarz, inequality

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