1950 AHSME Problem 39

Given the series 2+1+\frac{1}{2}+\frac{1}{4}+... and the following five statements:

(1) the sum increases without limit

(2) the sum decreases without limit

(3) the difference between any term of the sequence and zero can be made less than any positive quantity no matter how small

(4) the difference between the sum and 4 can be made less than any positive quantity no matter how small

(5) the sum approaches a limit

Of these statements, the correct ones are:

\textbf{(A)}\ \text{Only }3\text{ and }4\qquad\textbf{(B)}\ \text{Only }5\qquad\textbf{(C)}\ \text{Only }2\text{ and }4\qquad\textbf{(D)}\ \text{Only }2,3\text{ and }4\qquad\textbf{(E)}\ \text{Only }4\text{ and }5

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