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

[bkc82]

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?

 

[robert Ihnot]

You got to look at the law of exponents: X^a*X^b=X^{a+b}. This comes about because, say X^4*X^2=(XXXX)(XX)=X^6.

See: http://www.gomath.com/htdocs/lesson/exponent_lesson1.htm

 

[bkc82]

I understand that part but where does the four come from?

 

[vsage]

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.