Help Factorial Partial Fraction Decomposition

Click For Summary

Homework Help Overview

The discussion revolves around the algebraic manipulation of factorial expressions, specifically focusing on the relationship between the expression n/(n+1)! and its proposed equivalence to (1/n) - (1/(n+1)!). The context is set within infinite series.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the validity of the original statement, with one participant providing a counterexample using n=3. Others attempt to clarify the algebraic steps involved in manipulating factorial expressions.

Discussion Status

The discussion is active, with participants questioning the correctness of the original statement and offering alternative expressions. Some participants express confusion regarding factorial notation, while others provide insights into the algebraic relationships.

Contextual Notes

There is a noted lack of experience with factorials among some participants, which may influence their understanding of the problem. Additionally, the original poster expresses being lost in the algebraic steps, indicating potential gaps in foundational knowledge.

danerape
Messages
31
Reaction score
0

Homework Statement



Show that n/(n+1)!=(1/n)-(1/(n+1)!)

I am totally lost on the algebraic steps taken to come to this conclusion. It is for an
Infinite series.

Thanks
 
Physics news on Phys.org
It's not true. For example, take n=3. Then
[tex]\frac{n}{(n+1)!} = \frac{3}{4!} = \frac{3}{24} = \frac{1}{8}[/tex]but
[tex]\frac{1}{n}-\frac{1}{(n+1)!} = \frac{1}{3}-\frac{1}{24} = \frac{8}{24}-\frac{1}{24} = \frac{7}{24}[/tex]
 
Wow, sorry. I meant n/(n+1)!=1/n! - 1/(n+1)!
 
It's easy to prove. In the LHS write n=(n+1)-1.
 
Wow, that is pretty obvious, I haven't had any experience with ! before this though. Thanks a lot!

Dane
 

Similar threads

  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
Replies
9
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 6 ·
Replies
6
Views
1K
  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K