Difference between revisions of "2008 AMC 12A Problems/Problem 19"
(New page: ==Problem== In the expansion of <math>\left(1 + x + x^2 + \cdots + x^{27}\right)\left(1 + x + x^2 + \cdots + x^{14}\right)^2</math>, what is the coefficient of <math>x^{28}</math>? <mat...) |
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Revision as of 13:54, 17 February 2008
Problem
In the expansion of
,
what is the coefficient of 
?
Solution
Let 
and 
. We are expanding 
.
Since there are 
terms in 
, there are 
ways to choose one term from each . The product of the selected terms is 
for some integer 
between 
and 
inclusive. For each 
, there is one and only one 
in 
. Since there is only one way to choose one term from each to get a product of 
, there are 
ways to choose one term from each and one term from to get a product of . Thus the coefficient of the term is 
.
See Also
| 2008 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 18 |
Followed by Problem 20 |
| 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 | |
| All AMC 12 Problems and Solutions | |
