Difference between revisions of "1991 AIME Problems/Problem 3"
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== Solution == | == Solution == | ||
| − | Let <math>0< | + | Let <math>0<x_{}^{}<1</math>. Then we may write <math>A_{k}^{}=\frac{N!}{k!(N-k)!}x^{k}=\frac{(N-k+1)!}{k!}x^{k}</math>. |
== See also == | == See also == | ||
{{AIME box|year=1991|num-b=2|num-a=4}} | {{AIME box|year=1991|num-b=2|num-a=4}} | ||
Revision as of 19:55, 20 April 2007
Problem
Expanding 
by the binomial theorem and doing no further manipulation gives
where 
for 
. For which 
is 
the largest?
Solution
Let 
. Then we may write 
.
See also
| 1991 AIME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
