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A power series of the form:

f(x+a)=f(a)+f′(a)x+f"(a)x2/2+f"′(a)x3/3!+... +f(n−1)(a)xn−1/(n−1)!+Rn

is called a Taylor series. Taylor's theorem states the conditions under which such a function will exist for a function f. R_n is a remainder term; it can be written in various forms; its value is usually small.