Question

(a) What is the difference between a sequence and a series? A series is an unordered list of numbers whereas a sequence is the sum of a list of numbers. A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers. A series is an ordered list of numbers whereas a sequence is the sum of a list of numbers. A sequence is an ordered list of numbers whereas a series is an unordered list of numbers. A sequence is an unordered list of numbers whereas a series is the sum of a list of numbers. (b) What is a convergent series? What is a divergent series? A series is divergent if the nth term converges to zero. A series is convergent if it is not divergent. A series is convergent if the nth term converges to zero. A series is divergent if it is not convergent. A convergent series is a series for which lim n → ∞ an exists. A series is convergent if it is not divergent. A series is convergent if the sequence of partial sums is a convergent sequence. A series is divergent if it is not convergent. A series is divergent if the sequence of partial sums is a convergent sequ

Answer 1

• (a) A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers.

• (b) A series is divergent if the sequence of partial sums is a convergent sequence. A series is divergent if it is not convergent.

Explanation:

A sequence is a list of ordered numbers. For example, 1, 2, 3, 4, 5.... is a sequence. The numbers are listed in a specific order when we count. In contrast, a series is the sum of the numbers in a sequence. For this multiple choice, choose the best answer that defines what a sequence is.

(a) What is the difference between a sequence and a series?

• A series is an unordered list of numbers whereas a sequence is the sum of a list of numbers.
• A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers.
• A series is an ordered list of numbers whereas a sequence is the sum of a list of numbers.
• A sequence is an ordered list of numbers whereas a series is an unordered list of numbers.
• A sequence is an unordered list of numbers whereas a series is the sum of a list of numbers.

When working with sequences and series, we look at what happens at negative and positive infinity. When a series converges, it approaches a finite number. When a series diverges, it does not approach a finite number but infinity.

(b) What is a convergent series? What is a divergent series?

• A series is divergent if the nth term converges to zero. A series is convergent if it is not divergent.
• A series is convergent if the nth term converges to zero. A series is divergent if it is not convergent.
• A convergent series is a series for which lim n → ∞ an exists. A series is convergent if it is not divergent.
• A series is convergent if the sequence of partial sums is a convergent sequence. A series is divergent if it is not convergent.

• A series is divergent if the sequence of partial sums is a convergent sequence. A series is divergent if it is not convergent.

Answer 2

(a) A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers.

(b) A series is divergent if it is not convergent. A convergent series is a series for which lim n → ∞ an exists.

Explanation:

(a) By definition, a sequence is a list of numbers which have been ordered and a series is a sum of a sequence of terms.

(b) In a convergent series the sum of the list of numbers is equal to a certain number, then in the limit when n → ∞ a numeric result is obtained (the limit exist).