MathDB
Miklos Schweitzer 1971_5

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October 29, 2008
real analysisreal analysis unsolved

Problem Statement

Let λ1≤λ2≤... \lambda_1 \leq \lambda_2 \leq... be a positive sequence and let K K be a constant such that ∑k=1n−1λk2<Kλn2  (n=1,2,...). \sum_{k=1}^{n-1} \lambda^2_k < K \lambda^2_n \;(n=1,2,...). Prove that there exists a constant K′ K' such that ∑k=1n−1λk<K′λn  (n=1,2,...). \sum_{k=1}^{n-1} \lambda_k < K' \lambda_n \;(n=1,2,...). L. Leindler
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