Difference between revisions of "1992 AIME Problems/Problem 4"
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== See also == | == See also == | ||
| + | * [[1992 AIME Problems/Problem 3 | Previous Problem]] | ||
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| + | * [[1992 AIME Problems/Problem 5 | Next Problem]] | ||
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* [[1992 AIME Problems]] | * [[1992 AIME Problems]] | ||
Revision as of 20:03, 6 November 2006
Problem
In Pascal's Triangle, each entry is the sum of the two entries above it. In which row of Pascal's Triangle do three consecutive entries occur that are in the ratio 
?
Solution
In Pascal's Triangle, we know that the binomial coefficients of the nth row are 
, 
,...,
. Let our row be the nth row such that the three consecutive entries are 
, 
, and 
.
After expanding and dividing one entry by another (to clean up the factorials), we see that 
and 
. Solving, 
SOMEONE PLEASE SAVE THE LATEX!
