This same topic can be viewed as part of calculus. A sequence s is simply a function defined on the set of natural numbers. So, every natural number 1, 2, 3, ... has its own member of the sequence ![s[1]](/cgi-bin/plot-formula.mpl?expression=s%5B1%5D&x=0003) , ![s[2]](/cgi-bin/plot-formula.mpl?expression=s%5B2%5D&x=0003) , ...
A series is related to a sequence. A series for a given sequence s, is another sequence S where every member ![S[n]](/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D&x=0003) is the sum of elements , , ..., ![s[n]](/cgi-bin/plot-formula.mpl?expression=s%5Bn%5D&x=0003) .
![S[n] = sum( s[i], i=1, n )](/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D+=+sum%28+s%5Bi%5D%2C+i=1%2C+n+%29&x=0003)
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