Difference between revisions of "1950 AHSME Problems/Problem 39"

(Created page with "==Problem== Given the series <math> 2\plus{}1\plus{}\frac {1}{2}\plus{}\frac {1}{4}\plus{}...</math> and the following five statements: (1) the sum increases without limit (2) t...")
 
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\textbf{(D)}\ \text{Only }2,3\text{ and }4 \qquad
 
\textbf{(D)}\ \text{Only }2,3\text{ and }4 \qquad
 
\textbf{(E)}\ \text{Only }4\text{ and }5</math>
 
\textbf{(E)}\ \text{Only }4\text{ and }5</math>
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==Solution==
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{{solution}}
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==See Also==
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{{AHSME 50p box|year=1950|num-b=38|num-a=40}}
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[[Category:Introductory Algebra Problems]]

Revision as of 08:39, 29 April 2012

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:

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

Solution

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See Also

1950 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 38
Followed by
Problem 40
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All AHSME Problems and Solutions
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