2011 AMC 12B Problems/Problem 17
Problem
Let , and for integers . What is the sum of the digits of ?
Solution
Proof by induction that :
For ,
Assume is true for n:
\[
Therefore, if it is true for n, then it is true for n+1; since it is also true for n = 1, it is true for all positive integers n.
, which is the 2011-digit number 8888...8889
The sum of the digits is 8 times 2010 plus 9, or
See also
2011 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 16 |
Followed by Problem 18 |
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All AMC 12 Problems and Solutions |
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