Show that the series converges

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Homework Help Overview

The discussion revolves around a series and its convergence properties, with participants analyzing a mathematical expression related to sequences and series.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the nature of the expression, with one suggesting it is a sequence rather than a series. There are attempts to explore convergence through bounding and increasing properties, as well as considerations of Riemann sums.

Discussion Status

The conversation is active, with various interpretations being explored. Some participants provide guidance on how to approach the convergence proof, while others question the classification of the mathematical expression.

Contextual Notes

There is some confusion regarding whether the expression is a series or a sequence, which may affect the approach to proving convergence. Additionally, the original poster expresses uncertainty about how to proceed with the proof.

soopo
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Homework Statement


The series is at http://img203.imageshack.us/i/snapshot1g.png/

The Attempt at a Solution



The LHS series diverges. However, the term 1/n seems to be make the series to converge.
However, I am not completely sure how to proceed in proving that the series converges.

I should first show that the series has a converging point.
Then I can show that the series converges.
 
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That isn't a series, it is a sequence.

[tex]a_n = \frac 1 n\left(\frac 1 2 + \frac 2 3 + ... + \frac n {n+1}\right)[/tex]

One way to prove a sequence converges is to show it is bounded above and increasing. Try that.
 
Its a riemann sum.
 
^ Clever! I missed the obvious.

[/thread hijack]
 
Ratio Test =) said:
Its a riemann sum.

I don't think it's really a Riemann sum. The kth term is (k/n)/(k+1). If it were a Riemann sum, that would be a function only of (k/n).
 

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