## convergenceConvergence is a property of some sequences and series. A sequence u is said to be convergent if there exists
a value _{i}u with the property that by choosing a large enough value
of i, we can make u as close as we wish to _{i}u.
In other words, convergence is the tendency of a sequence toward a limit.
In the case of a series, it is the tending toward of the consecutive partial
sums of the series toward a limit. A sequence or series which does not converge
is said to diverge. For example, for the series 1 + (½) + (½)the sum of the first two terms is 1.5, the first three 1.75, and the first four 1.875; as more and more terms are evaluated, the sum approaches the limiting value of (i.e., converges on) 2. ## Related categories• CALCULUS AND ANALYSIS• SERIES AND SEQUENCES | |||||

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