Understanding Sequences and Series

Both are sums of numbers.

Both are lists of numbers.

A sequence is a list, while a series is a sum.

A sequence is a sum, while a series is a list.

As a product of its terms.

As a function of its index.

As a sum of its terms.

As a difference of its terms.

The product of all terms in a sequence.

The average of all terms in a sequence.

The difference between the first and last terms of a sequence.

The sum of the first n terms of a sequence.

The series terms become zero.

The series has an infinite sum.

The series terms become negative.

The series has a finite sum.

Both have real number domains.

Both have integer domains.

Sequences have integer domains, functions have real number domains.

Sequences have real number domains, functions have integer domains.

Product

Limit

Integral

Derivative

It has a common sum.

It has a common product.

It has a common ratio.

It has a common difference.

When the common ratio is greater than one.

When the common ratio is negative.

When the common ratio is less than one.

When the common ratio is equal to one.

a / (1 - r)

a * (1 + r)

a + r

a - r

The series becomes constant.

The series converges.

The series becomes zero.

The series diverges.