We went through exercises that asked Sam to write an Arithmetic Series in Summation Notation. I showed her how to find the explicit formula for the Series.
I introduced a Geometric Series, which is the sum of terms of geometric sequence. I showed her the sum formula for finite and infinite geometric series. They converge (get closer and closer to a sum) if the absolute value of the common ratio is <1. A series diverges if the absolute value of the common ratio is >1. We can identify if an infinite geometric series converges or diverges based on the common ratio.