Radius of Convergence for Series: 3n+3 vs 3n+3!

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Homework Help Overview

The discussion revolves around determining the radius of convergence for a series involving factorial expressions, specifically comparing (3n+3)! and (3n)! with additional terms. Participants are exploring the implications of these expressions on convergence.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to clarify the relationship between (3n+3)! and (3n)! and are questioning the validity of their assumptions. There is also discussion about using the ratio test and concerns about the notation used for the series.

Discussion Status

The conversation is ongoing, with some participants providing insights into the factorial expressions and suggesting the use of the ratio test. However, there is no consensus on the approach to take, and some participants express confusion regarding the notation and setup.

Contextual Notes

Participants are navigating issues related to notation clarity and the specific terms of the series being analyzed. There is an indication that the original poster is facing challenges with the convergence question, which may be compounded by the complexity of the factorial expressions involved.

jack.o
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Is (3n+3)!=(3n)!+3!
? probably obvious but I'm not certain. Trying to work out a radius of convergence for a series.
 
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jack.o said:
Is (3n+3)!=(3n)!+3!
? probably obvious but I'm not certain. Trying to work out a radius of convergence for a series.

No. It is the product from i=1 to 3 of (3n!)*(3n+i)
 
You can quickly verify this for yourself by checking the case where n = 1.
 
(3n+3)!=(3n+3)(3n+2)(3n+1)(3n)(3n-1)...(6)(5)(4)(3)(2)(1)
 
Ok, this convergence question still has me stuck

[tex]\stackrel{\infty}{\stackrel{\sum}{n=0}}[/tex][tex]\stackrel{\chi^{n}}{\overline{(3n)!}}[/tex]

Got the n+1 term and tried dividing the nth term by the nth+1 but does not seem to cancel nicely.
 
Last edited:
If [tex]\stackrel{\chi^{n}}{(3n)!}[/tex] is not a fraction with the line missing, then I have no idea what you mean.
 
It is meant to be a fraction, not used to the equation editor software here.
 
Jack - you were on the right track by figuring out the n+1 term. Use the ratio test. You should see fairly readily that the series converges to 0 as n goes to infinity.
 

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