What is the operation between row 2 and row 3 in the convergence of this series?

Click For Summary

Homework Help Overview

The discussion revolves around the convergence of a series defined by a term Un. Participants are examining the operations involved in the transition between two specific rows in a provided solution, particularly questioning the nature of these operations and their relation to Taylor series expansion.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to understand the operation between row 2 and row 3 in the context of series convergence, questioning its connection to Taylor series. Some participants provide insights regarding the Taylor series expansion of a specific function.

Discussion Status

The discussion includes some guidance on the nature of the operation, with references to Taylor series expansion. However, the original poster's understanding appears incomplete, and further clarification may be needed.

Contextual Notes

Participants note that familiarity with Taylor expansion formulas for fractional powers may not be necessary for understanding the operation in question.

kapitan90
Messages
32
Reaction score
0

Homework Statement



I need to examine convergence of series with a term Un given below.

The solution is given, but I can't understand what happens between row 2 and row 3.
What kind of operation is that, does it have something in common with Taylor series expansion?
[PLAIN]http://img805.imageshack.us/img805/4619/convergence.png
 
Last edited by a moderator:
Physics news on Phys.org
It is exactly the taylor series expansion of [tex]\left(1+\frac{1}{n^3}\right)^{1/3}[/tex]
 
Ok, thanks!
 
BTW, you don't need to know it by heart. You expand it using the Taylor Expansion formulas for fractional powers.
 

Similar threads

  • · Replies 11 ·
Replies
11
Views
3K
Replies
29
Views
5K
  • · Replies 10 ·
Replies
10
Views
4K
  • · Replies 18 ·
Replies
18
Views
3K
Replies
6
Views
2K
  • · Replies 22 ·
Replies
22
Views
3K
  • · Replies 18 ·
Replies
18
Views
3K
Replies
8
Views
1K
  • · Replies 26 ·
Replies
26
Views
3K
  • · Replies 2 ·
Replies
2
Views
1K