Answer
$$\frac{1}{1+4x}.$$
Work Step by Step
Since we have$$
1-4 x+4^{2} x^{2}-4^{3} x^{3}+4^{4} x^{4}-4^{5} x^{5}+\cdots\\
=1-4 x+(4 x)^{2}-(4 x)^{3}+(4 x)^{4}-(4 x)^{5}+\cdots
$$
Then by using Table 2, we see that this is Maclaurin series of the function
$$\frac{1}{1+4x}.$$
