2000 Pan African MO Problems/Problem 2
Problem
Define the polynomials by: Find the coefficient of in .
Solution
Note that , , and . Thus, we can suspect that and use induction to prove it.
The base case works because . For the inductive step, assume that . Thus,
Therefore, , so
To find the coefficient of , we can use the Binomial Theorem. The coefficient of is
See Also
2000 Pan African MO (Problems) | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
All Pan African MO Problems and Solutions |