## Series and Their Notations

### Learning Objectives

• 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.

### Glossary

annuity
an investment in which the purchaser makes a sequence of periodic, equal payments
arithmetic series
the sum of the terms in an arithmetic sequence
diverge
a series is said to diverge if the sum is not a real number
geometric series
the sum of the terms in a geometric sequence
index of summation
in summation notation, the variable used in the explicit formula for the terms of a series and written below the sigma with the lower limit of summation
infinite series
the sum of the terms in an infinite sequence
lower limit of summation
the number used in the explicit formula to find the first term in a series
nth partial sum
the sum of the first$n$terms of a sequence
series
the sum of the terms in a sequence
summation notation
a notation for series using the Greek letter sigma; it includes an explicit formula and specifies the first and last terms in the series
upper limit of summation
the number used in the explicit formula to find the last term in a series