Question

Ask Your Teacher (a) What is the difference between a sequence and a series? A sequence is an unordered list of numbers whereas a series 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 sequence is an ordered list of numbers whereas a series is an unordered list of numbers. A series is an unordered list of numbers whereas a sequence 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. (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 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 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.

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 convergent if the sequence of partial sums is a convergent sequence, that is tends to a limit.

A series is divergent if it is not convergent.

Explanation:

(b) An example of a divergent series is the arithmetic series 2+ 4+6+8+10+...

The sum keeps increasing without bounds.

An example of a convergent series is 100 + 50, +25 + 12.5 +... a geometric series with common ratio 0.5 whose sum tends to a limit. The limit of this series is a1 / (1 - r) = 100 / (1 - 0.5) = 200.