Maclaurin series is infinite power series of n-th term equal to:
an = (f(n)(0))*xn/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 Rn at infinity equals 0 and:
Rn = (f(n)(c))*xn/n!
where c is between 0 and x, then:
f(x) = f(0) + a1 + a2 + ...