Identify whether the function is finitely many or infinitely many terms in Maclaurin's series

Consider the Maclaurin's series of (1+x)
(a) are there finitely many or infinitely many terms in this Maclaurin's series? Justify your answer..
(b) Write down all of the terms if there are finitely many, and the first four terms if there are infinitely many
(c) Use your answer in part (b) to estimate (1.2)^(1)

Note that f(x) = 1+x, f '(x) = 1, and f^(k)(x) = 0 for all k > 1.
==> f(0) = 1, f '(0) = 1, and f^(k)(0) = 0 for all k > 1.

Hence, f(x) has Macularin Series 1 + 1x + 0 = 1 + x (itself!)
So, this series has only finitely many terms.

Letting x = 0.2 yields
(1.2)^1 = 1 + 0.2 = 1.2 (surprise!)

I hope this helps!

Every polynomial in one variable is its own MacLaurin series.:)