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Revision difference : sum of series
Version 4 Version 3
If a series $\sum_{n = 1}^\infty a_n$ of real or complex numbers is convergent and the limit of its partial sums is $S$, then $S$ is the {\em sum of the series}. \,This circumstance may be denoted by If a series $\sum_{n = 1}^\infty a_n$ of real or complex numbers is convergent and the limit of its partial sums is $S$, then $S$ is the {\em sum of the series}.
$$\sum_{n = 1}^\infty a_n = S$$
or
$$a_1+a_2+a_3+... = S.$$
The sum of the series is equal to the sum of a partial sum and the corresponding remainder term. The sum of the series is equal to the sum of a partial sum and the corresponding remainder term.