1962 AHSME Problems/Problem 12: Difference between revisions
Created page with "==Problem== When <math>\left ( 1 - \frac{1}{a} \right ) ^6</math> is expanded the sum of the last three coefficients is: <math> \textbf{(A)}\ 22\qquad\textbf{(B)}\ 11\qquad\text..." |
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==Solution== | ==Solution== | ||
This is equivalent to <math>\frac{(a-1)^6}{a^6}.</math> | |||
Its expansion has 7 terms, whose coefficients are the same as those of <math>(a-1)^6</math>. | |||
By the Binomial Theorem, the sum of the last three coefficients is | |||
<math>\binom{6}{2}-\binom{6}{1}+\binom{6}{0}=15-6+1=\boxed{10 \textbf{ (C)}}</math>. | |||
==See Also== | |||
{{AHSME 40p box|year=1962|before=Problem 11|num-a=13}} | |||
[[Category:Introductory Algebra Problems]] | |||
{{MAA Notice}} | |||
Latest revision as of 21:15, 3 October 2014
Problem
When 
is expanded the sum of the last three coefficients is:
Solution
This is equivalent to 
Its expansion has 7 terms, whose coefficients are the same as those of 
.
By the Binomial Theorem, the sum of the last three coefficients is
.
See Also
| 1962 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
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| All AHSME Problems and Solutions | ||
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