2007 iTest Problems/Problem 58
The following problem is from the Ultimate Question of the 2007 iTest, where solving this problem required the answer of a previous problem. When the problem is rewritten, the T-value is substituted.
Problem
For natural numbers , we define Compute the value of .
Solution
The function can be rewritten as
Let . With the substitution, each similar part becomes Performing polynomial division results in When or , then is close to zero, which means that would be the same for a given when or . Thus, .
That means , and that equals
See Also
2007 iTest (Problems, Answer Key) | ||
Preceded by: Problem 57 |
Followed by: Problem 59 | |
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