Problem 6 · 2009 Math Kangaroo
Medium
Fractions, Decimals & Percents
grouping
What is the value of 12·23·34·…·910·1000?
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Answer: C — 100
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Hint 1 of 2
Write the product as one long fraction and look at what cancels.
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Hint 2 of 2
Each numerator matches the previous denominator — it telescopes.
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Approach: telescoping product of fractions
- In ½·⅔·¾·…·9⁄10, every numerator cancels the next denominator.
- Only the first numerator 1 and the last denominator 10 survive, giving 1/10.
- Then (1/10)·1000 = 100.
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