They are used to approximate functions like sin(x) and cos(x), so a calculator, for example, can calculate sin (x) and cos(x), which are infinite series functions.
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An infinite series of points
The Fourier series is a specific type of infinite mathematical series involving trigonometric functions that are used in applied mathematics. It makes use of the relationships of the sine and cosine functions.
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No. ∑(1/n) diverges. It is the special infinite series known as the "harmonic series."
A power series in mathematics (in one variable) is an infinite series of a certain form. It normally appears as the Taylor series of a known function.