Concept preview

What you will be able to do

1. 01Understand a series as the sum of the terms of a sequence
2. 02Use the arithmetic and geometric sum formulas
3. 03Sum an infinite geometric series and apply it to real problems

So far we have listed terms. A series is what you get when you add those terms up. We write the sum of the first $n$ terms as $S_n = t_1 + t_2 + t_3 + \dots + t_n$. So for the sequence $3, 7, 11, 15$, the series $S_4 = 3 + 7 + 11 + 15 = 36$. Small sums you can just add by hand — but for hundreds of terms we need a shortcut, and the shortcuts are wonderfully clever.