Nth partial sum

Definition

The nth partial sum of a series is the sum of the first n terms of that series. It provides an approximation to the total sum of an infinite series by summing a finite number of terms.

5 Must Know Facts For Your Next Test

1. The nth partial sum is denoted as $S_n$.
2. To find $S_n$, you sum the first n terms: $S_n = a_1 + a_2 + \cdots + a_n$.
3. $S_n$ can be used to approximate the value of an infinite series if it converges.
4. In arithmetic series, $S_n = \frac{n}{2} (a_1 + a_n)$ where $a_1$ is the first term and $a_n$ is the nth term.
5. In geometric series, $S_n = a \frac{1-r^n}{1-r}$ for $r \neq 1$, where $a$ is the first term and $r$ is the common ratio.

Review Questions

• What is the formula for finding the nth partial sum in an arithmetic series?
• How do you calculate the nth partial sum for a geometric series?
• What does it mean if the sequence of partial sums converges?

Related terms

Series:

A sequence of numbers that are added together, often expressed in sigma notation.

Convergence:

A property of a series where its sequence of partial sums approaches a specific value as n approaches infinity.

Infinite Series:

A series that continues indefinitely without terminating.