Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 5.8 AIME, harder Find the answer

13. Given the sequence $\left\{a_{n}\right\}$ , the sum of the first $n$ terms $S_{n}$ satisfies $S_{n}=2 a_{n}+(-1)^{n}, n \geqslant 1$
(1) Find the general term formula for the sequence $\left\{a_{n}\right\}$ ;
(2) Prove: For any integer $m>4$ , $\frac{1}{a_{4}}+\frac{1}{a_{5}}+\cdots+\frac{1}{a_{m}}<\frac{7}{8}$ .

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

None

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None

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