Convergent Series: Introduction & Identification

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Discussion Overview

The discussion revolves around the concept of convergent series, specifically focusing on how to identify whether a series converges. The scope includes theoretical aspects and practical identification methods.

Discussion Character

  • Homework-related, Technical explanation

Main Points Raised

  • One participant requests an explanation of convergent series and how to identify them.
  • Another participant suggests that the inquiry is not appropriate for a forum and recommends formal study or research through books or online resources.
  • A different participant recommends working through Spivak's Calculus as a resource for understanding the topic.
  • Another participant defines a convergent series as one that converges to a finite value and mentions several tests for convergence, including the "number of terms" test and the "limit" test, while noting that there are additional tests without detailing them.

Areas of Agreement / Disagreement

There is no consensus on how to approach the question, with some participants suggesting formal study and others providing definitions and tests for convergence.

Contextual Notes

Some responses imply a need for foundational knowledge in analysis, and there are varying levels of detail provided regarding the identification of convergent series.

hsaimul
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I need to know about converge series.For example how to identify a converge series.Plz explain.
 
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hsaimul said:
I need to know about converge series.For example how to identify a converge series.Plz explain.



This is not a consult question. You need either to take a course in basic analysis, or read a book or, at least, check google under "infinite series".

DonAntonio
 
Get Spivaks Calculus and work through it.
 
A convergent series is a series that converges to a finite value. There are several tests to find if a given series is convergent. First, there's the "number of terms" test. If your series has a finite number of terms, it's convergent. Easily done. There's also the "limit" test. If the terms in your series don't tend to zero, it's not convergent.

There are other tests that can help you out here, but I don't feel like enumerating all of them.
 

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