Problem 1 · 2010 Math Kangaroo
Medium
Arithmetic & Operations
arithmetic-series
In the picture we see that 1 + 3 + 5 + 7 = 4×4. How big is 1 + 3 + 5 + 7 + … + 17 + 19?
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Answer: A — 10×10
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Hint 1 of 2
The picture shows the sum of the first few odd numbers makes a perfect square.
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Hint 2 of 2
Count how many odd numbers you are adding from 1 up to 19.
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Approach: sum of the first n odd numbers is n squared
- The odd numbers 1, 3, 5, ..., 19 are the first ten odd numbers.
- The sum of the first n odd numbers equals n×n.
- Here n = 10, so the total is 10×10.
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