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.