Chapter 14.2, Problem 1PE

(a)

To determine

To fill: The blanks provided in the statement, “A _________ sequence is a function whose domain is the set of positive integers. A_______ sequence is a function whose domain is the set of the first n positive integers.”

(b)

To determine

To fill: The blanks provided in the statement, “Given a sequence, the values $a_1,a_2,a_3,$ and so on are called the ______ of the sequence. The expression an defines the ____ term (or general term) of the sequence.”

(c)

To determine

To fill: The blank provided in the statement, “In an _____ sequence, consecutive terms alternate is sign.”

(d)

To determine

To fill: The blank provided in the statement, “A sum of a sequence is called a ____.”

(e)

To determine

To fill: The blank provided in the statement, “To represent of a sum of terms, ____ notation is often used and is represented by the Greek letter ${\displaystyle \sum }$”.

(f)

To determine

To fill: The blank provided in the statement, “Given the sum ${\displaystyle \sum _{n=1}^5{n}^2}$, the letter n is called the _______ of summation. In expanded form, this series is ${\left(1\right)}^2+{\left(2\right)}^2+\_\_\_\_=55$ .”