Question

What is the difference between a sequence and a series in math?

Answer 1

See explanation

Explanation:

A sequence is a function `f:NN->RR`.
A series is a sequence of sums of terms of a sequence.

For example

`a_n=1/n` is a sequence, its terms are: `1/2;1/3;1/4;...`

This sequence is convergent because `lim_{n->+oo}(1/n)=0`.

Corresponding series would be:

`b_n=Sigma_{i=1}^{n}(1/n)`

We can calculate that:

`b_1=1/2`

`b_2=1/2+1/3=5/6`

`b_3=1/2+1/3+1/4=13/12`

The series is divergent.