- #31
Jbreezy
- 582
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Got it thanks to all.
Series Convergence Verification
- Thread starter Jbreezy
- Start date
-
- Tags
- Convergence
Click For Summary
Homework Help Overview
The discussion revolves around verifying the convergence of the infinite series \(\sum_{n=1}^\infty\frac{1}{n(n+1)}\). Participants are exploring the relationship between the series' terms and the limits involved in determining convergence.
Discussion Character
- Exploratory, Assumption checking, Mathematical reasoning
Approaches and Questions Raised
- Participants discuss the use of partial fractions and the limit of the series' terms. There is confusion regarding the transition from \(1/n - 1/(n+1)\) to \(1 - 1/(n+1)\) and the necessity of taking limits of different expressions.
Discussion Status
The discussion is ongoing, with participants providing insights into the simplification of the series and questioning the reasoning behind the limits taken. Some guidance has been offered regarding the use of partial sums and the nature of telescoping series, but no consensus has been reached on the specific limit to evaluate.
Contextual Notes
Participants are grappling with the implications of the series' structure and the definitions of convergence, as well as the specific steps taken in their textbooks versus their own calculations.
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