1950 AHSME Problems/Problem 39

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Problem

Given the series $2\plus{}1\plus{}\frac {1}{2}\plus{}\frac {1}{4}\plus{}...$ (Error compiling LaTeX. ! Undefined control sequence.) 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 statments, the correct ones are:

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

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