**Maclaurin series**is infinite power series of n-th term equal to:

a

_{n}= (f

^{(n)}(0))*x

^{n}/n!

where f

^{(n)}(0) is value of n-th derivative of certain function f(x) for x = 0.

A Maclaurin series is a Taylor series expansion of a function about 0.

It can be proven, that if function f(x) is differentiable infinite amount of times in certain neighbourhood of x = 0 and limit of R

_{n}at infinity equals 0 and:

R

_{n}= (f

^{(n)}(c))*x

^{n}/n!

where c is between 0 and x, then:

f(x) = f(0) + a

_{1}+ a

_{2}+ ...

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