5^(n+1) - 1 = 4*5^n + 5^n -1 ?

  • Context: Undergrad 
  • Thread starter Thread starter bkc82
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around the equation 5^(n+1) - 1 = 4*5^n + 5^n - 1, specifically focusing on understanding the steps and reasoning behind the equality as presented in a textbook. Participants are seeking clarification on the mathematical manipulation involved.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant requests a demonstration of how the two sides of the equation are equal, indicating a lack of clarity in the textbook's explanation.
  • Another participant references the law of exponents to explain the multiplication of terms, but does not directly address the specific equation in question.
  • A participant questions the origin of the coefficient '4' in the equation, suggesting it appears arbitrary and is only present to complicate the understanding.
  • Further elaboration is provided that the equation can be expressed in different forms, such as 5^(n+1) = 5*5^n, which leads to alternative representations involving different coefficients.

Areas of Agreement / Disagreement

There is no consensus on the reasoning behind the coefficient '4' in the equation, with some participants expressing confusion and others suggesting it may not have a significant purpose.

Contextual Notes

The discussion highlights a lack of clarity in the steps leading to the equality, with participants expressing uncertainty about the role of specific coefficients and the manipulation of terms.

bkc82
Messages
6
Reaction score
0
5^(n+1) - 1 = 4*5^n + 5^n -1 ??

This is what my book says but it does not show the math in between the steps so i can't seem to grasp it. Anyone want to show me how they are equal?
 
Mathematics news on Phys.org
You got to look at the law of exponents: [tex]X^a*X^b=X^{a+b}.[/tex] This comes about because, say X^4*X^2=(XXXX)(XX)=X^6.

See: http://www.gomath.com/htdocs/lesson/exponent_lesson1.htm
 
Last edited by a moderator:
I understand that part but where does the four come from?
 
The 4 seems arbitrary to me but it works as long as you have the 1 coefficient of the other 5^n term. Here's what I mean

5^(n+1) = 5*5^n yes?
This also equals

4*5^n + 1*5^n

or 3*5^n + 2*5^n

It's not there for any reason other than to confuzzle you from what I see.
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 59 ·
2
Replies
59
Views
232K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 7 ·
Replies
7
Views
4K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 55 ·
2
Replies
55
Views
8K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 20 ·
Replies
20
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K