Difference between revisions of "2018 AMC 12B Problems/Problem 9"
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== Solution 2 == | == Solution 2 == | ||
− | <cmath> \sum^{100}_{i=1} \sum^{100}_{j=1} (i+j) = \sum^{100}_{i=1} 100i+5050 = 100 \cdot 5050 + 5050 \cdot 100 = \boxed{1,010,000} </cmath> | + | <cmath> \sum^{100}_{i=1} \sum^{100}_{j=1} (i+j) = \sum^{100}_{i=1} 100i+5050 = 100 \cdot 5050 + 5050 \cdot 100 = \boxed{1,010,000} </cmath> |
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== Solution 3 == | == Solution 3 == |
Revision as of 02:08, 19 February 2018
Problem
What is
Solution 1
We can start by writing out the first couple of terms:
Looking at the second terms in the parentheses, we can see that occurs
times. It goes horizontally and exists
times vertically.
Looking at the first terms in the parentheses, we can see that
occurs
times. It goes vertically and exists
times horizontally.
Thus, we have:
This gives us:
Solution 2
Solution 3
See Also
2018 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 8 |
Followed by Problem 10 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.