Difference between revisions of "2000 Pan African MO Problems/Problem 2"
Rockmanex3 (talk | contribs) (Solution to Problem 2 -- if an AIME problem did have the 0-999 limit) |
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Latest revision as of 14:05, 14 December 2019
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 |