The sequence of terms converges to $0$, as the the sequence is convergent in the standard sense. One can quickly prove this as $\left|(-1)^{n-1}\frac{-2n-1}{n^2+n}\right|=\left|\frac{2n+1}{n^2+n} \right|\leq \left|\frac{2}{n+1}\right|<\varepsilon$, but this doesn't necessarily imply that the series is Cesaro summable though. Any insights?
2026-02-23 19:43:19.1771875799
Is the series $\sum^{\infty}_{n=1}(-1)^{n-1}\frac{-2n-1}{n^2+n}$ Cesaro summable?
31 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in REAL-ANALYSIS
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