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Mar 26,  · Because the Taylor series is a form of power series, every Taylor series also has an interval of convergence. When this interval is the entire set of real numbers, you can use the series to find the value of f (x) for every real value of x. However, when the interval of convergence for a Taylor series is bounded — that is, when it diverges for some values of .

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If the partial sums Sn of an infinite series tend to a limit S, the series is called convergent. Otherwise it is called divergent. The limiting value S is called the sum of the series Lets look at some examples of convergent and divergence series examples. Let us consider two series Convergent series example The sum of this series is finite.