Introduction to Series and Their Notations

Learning Objectives

By the end of this section, you will be able to:

• Use summation notation.
• Use the formula for the sum of the ﬁrst $n$ terms of an arithmetic series.
• Use the formula for the sum of the ﬁrst $n$ terms of a geometric series.
• Use the formula for the sum of an inﬁnite geometric series.
• Solve annuity problems.

A couple decides to start a college fund for their daughter. They plan to invest \$50 in the fund each month. The fund pays 6% annual interest, compounded monthly. How much money will they have saved when their daughter is ready to start college in 6 years? In this section, we will learn how to answer this question. To do so, we need to consider the amount of money invested and the amount of interest earned.