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 an unordered 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 unordered 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. (b) What is a convergent series? What is a divergent series? 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 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 → [infinity] an exists. A series is convergent if it is not divergent. 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 divergent if the nth term converges to zero. 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. A series is divergent if it is not convergent.

Explanation:

A sequence is a list of numbers in which the order of numbers listed is important, so for instance;

1, 2, 3, 4, 5, ...

is one sequence, and

2, 1, 4, 3, 6, 5, ...

is an entirely different sequence.

A series is a sum of numbers in a list. For example,

1 + 1/2 + 1/4 + 1/8 + 1/16 + ...

is an example of a series. A series is composed of a sequence of

terms that are added up.

A divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit. If a series converges, the individual terms of the series must approach zero.