Difference between revisions of "1957 AHSME Problems/Problem 30"
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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 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
