◀ ▲ ▶Branches / Analysis / Proposition: Monotony Criterion
Proposition: Monotony Criterion
An infinite series \(\sum_{k=0}^\infty x_k\) with non-negative terms \(x_k\ge 0\) for all \(k\in\mathbb N\) is convergent if and only if the sequence \((s_n)_{n\in\mathbb N}\) of its partial sums \(s_n:=\sum_{k=0}^n x_k\) is bounded.
Table of Contents
Corollaries: 1 Proofs: 1
Mentioned in:
Proofs: 1 2
Thank you to the contributors under CC BY-SA 4.0!
- Github:
-
References
Bibliography
- Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983