1965 AHSME Problem 18

If 1 - y is used as an approximation to the value of \frac {1}{1 + y}, |y| < 1, the ratio of the error made to the correct value is:

\textbf{(A)}\ y \qquad \textbf{(B) }\ y^2 \qquad \textbf{(C) }\ \frac {1}{1 + y} \qquad \textbf{(D) }\ \frac{y}{1+y}\qquad \textbf{(E) }\ \frac{y^2}{1+y}\qquad

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.