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Power series

A useful application of the theory of sums of series is for power series. These are sums of series of the form f (z) = ∑ n = 0 ∞ c n z n. {\displaystyle f(z)=\sum _{n=0}^{\infty }c_{n}z^{n}.} Often z {\displaystyle z} is thought of as a complex number, and a suitable notion of convergence of complex sequences is needed. The set of values of z ∈ C {\displaystyle z\in \mathbb {C} } for which the series sum converges is a circle, with its radius known as the radius of convergence.