What Are Ratio Test Examples and How Do Notations Affect Cancellations?

[rcmango]

Homework Statement

I'm attached a pic of an example.

just wondering when i was trying the ratio test with a problem, i noticed numbers displayed in the pic.

is another way to write those examples like this: 5*5 or (x-1)*(x-1) ?

is that all the n+1 means?

also if there was something like: (n^7) / (n+1)^7 how can those cancel?
sorry about notation there.

thanks

Homework Equations

The Attempt at a Solution

 

[rcmango]

nevermind.

 

[danni7070]

\frac{n^7}{(n+1)^7} behaves like \frac{n^7}{n^7} for large n

so in your example it's just 1 if the limit goes to infinity. Can you see it?