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

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Answer 1 · 2015-11-15T21:31:59

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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.