Don't understand how they simplified this (ratio test)

[quickclick330]

Don't understand how they simplified this...(ratio test)

I'm studying for my exam and I was looking at this example:

I'm not really sure how they get from here :

to here:

If someone could explain how they simplified this to me that would be fantastic...i'm really trying to understand series but sometimes the algebra stuff holds me up :-(.

 

[SNOOTCHIEBOOCHEE]

You are basically just dividing like terms, so you subtract exponents

(-3)^n+2 / (-3)^n+1 = (-3)^ ((n+2)-(n+1)) = -3

2^3n / 2^(3n+3) = 2^((3n) -(3n+3)) = 2^-3

hope that helps

 

[quickclick330]

yes that helps...thank you :-)

 

[quickclick330]

actually that helped a lot... thank you thank you!