Not understanding calc proof of series

[isukatphysics69]

Homework Statement

Homework Equations

The Attempt at a Solution

I don't understand why for the first part where the series goes up until ar^n-1, it cannot just go up until arⁿ.. why will that first series always go up until ar^n-1 until it is multiplied by r?

 

[kuruman]

I don't understand why for the first part where the series goes up until arn-1, it cannot just go up until arn.. why will that first series always go up until arn-1 until it is multiplied by r?

By convention, $S_n$ denotes the sum of the first $n$ terms. The exponents start at $0$ and end at $n-1$. If you count the terms, you will see that their total number is $n$.

 

[isukatphysics69]

By convention, $S_n$ denotes the sum of the first $n$ terms. The exponents start at $0$ and end at $n-1$. If you count the terms, you will see that their total number is $n$.

i see, thank you!

 

[isukatphysics69]

i feel physically sick thinking about this calc 2 final

 

[kuruman]

i feel physically sick thinking about this calc 2 final

It, too, shall pass. Believe me, I've been there, done that. Good luck.