1993 AIME Problems/Problem 5
From AoPSWiki
Problem
Let 
. For integers 
, define 
. What is the coefficient of 
in 
?
Solution
Notice that
Using the formula for the sum of the first 
numbers, 
. Therefore, 
Substituting 
into the function definition, we get 
. We only need the coefficients of the linear terms, which we can find by the binomial theorem.
will have a linear term of 
.
will have a linear term of 
.
will have a linear term of 
.
Adding up the coefficients, we get 
.
See also
| 1993 AIME (Problems • Resources) | ||
| Preceded by Problem 4 | Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
