Chapter B, Problem 2AYU

If $a_1,a_2,\mathrm{...},a_n,\mathrm{...}$ is some collection of numbers, the expression

${\displaystyle \underset{k=1}{\overset{\infty }{\sum }}{a}_k=a_1+a_2+\cdot \cdot \cdot }+a_n+\cdot \cdot \cdot$ is called $a\left(n\right)$ _____ _____.

To determine

To fill: If $a_1, a_2, \dots \mathrm{..}, a_n, \dots .$ is some collection of numbers, the expression ${\displaystyle \sum _{k = 1}^{\infty }{a}_1 + a_2 + \cdots + a_n + \cdots }$ is called a(n) ______ __________.

Answer to Problem 2AYU

Solution:

If $a_1, a_2, \dots \mathrm{..}, a_n, \dots .$ is some collection of numbers, the expression ${\displaystyle \sum _{k = 1}^{\infty }{a}_1 + a_2 + \cdots + a_n + \cdots }$ is called a (n) infinite series.

Explanation of Solution

If $a_1, a_2, \dots \mathrm{..}, a_n, \dots .$ is some collection of numbers, the expression ${\displaystyle \sum _{k = 1}^{\infty }{a}_1 + a_2 + \cdots + a_n + \cdots }$ is called a (n) infinite series. The numbers $a_1, a_2, \dots \mathrm{..}, a_n, \dots .$

are called terms and the number $a_n$ is called the $\text{n}$th term or general term.