#Sequences convergence series
In the next theorem, Part ii) is really a corollary. A series is convergent (or converges) if the sequence of its partial sums tends to a limit that means that, when adding one after the other in the order given by the indices, one gets partial sums that become closer and closer to a given number.
In mathematics, convergence tests are methods of testing for the convergence, conditional convergence, absolute convergence, interval of convergence or divergence of an infinite series ∑ n = 1 ∞ a n converges. Theorems involving multiplication and division of terms in convergent sequences are a bit harder to prove.
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