1957 AHSME Problems/Problem 30: Difference between revisions
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<math>c= | == Problem == | ||
The sum of the squares of the first n positive integers is given by the expression <math>\frac{n(n + c)(2n + k)}{6}</math>, | |||
if <math>c</math> and <math>k</math> are, respectively: | |||
<math>\textbf{(A)}\ {1}\text{ and }{2} \qquad \textbf{(B)}\ {3}\text{ and }{5}\qquad \textbf{(C)}\ {2}\text{ and }{2}\qquad\textbf{(D)}\ {1}\text{ and }{1}\qquad\textbf{(E)}\ {2}\text{ and }{1} </math> | |||
== Solution == | |||
When <math>n=1</math>, the value of the given expression must be <math>1^2=1</math>. Plugging in the values given by the answer choices, we see that the only option that returns <math>1</math> when <math>n=1</math> is <math>\boxed{\textbf{(D) }1 \text{ and } 1}</math>. | |||
== See Also == | |||
{{AHSME 50p box|year=1957|num-b=29|num-a=31}} | |||
{{MAA Notice}} | |||
[[Category:AHSME]][[Category:AHSME Problems]] | |||
Latest revision as of 17:07, 25 July 2024
Problem
The sum of the squares of the first n positive integers is given by the expression 
,
if 
and 
are, respectively:
Solution
When 
, the value of the given expression must be 
. Plugging in the values given by the answer choices, we see that the only option that returns 
when is 
.
See Also
| 1957 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 29 |
Followed by Problem 31 | |
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