1993 AIME Problems/Problem 5
Problem
Let . For integers
, define
. What is the coefficient of
in
?
Solution
Notice that . Using the formula for the sum of the first
numbers,
. Thus,
.
Substitute into the equation, so we get
. The cubic will have a term of
. The square will have a term of
. The linear part will have a term of
. Adding up the coefficients, we get
.
See also
1993 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |