5th Grade Normal Difficulty Problem Problem of the Week 12/3/2018
Algebra
Level
2
What is
(1 1/1) times (1 1/2) times (1 1/3) times (1 1/4) times (1 1/5)... (1 1/1000) ?
1000/1
1001/1
1000/1001
1/1000
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1 solution
You have to use telescoping! 1 1/1 equals 2/1, 1 1/2 equals 3/2, and so on all the way until 1001/1000. Cross out the 2,3, 4, because they are repeated both in the numerator and the denominator. What's left? 1001 in the numerator and 1 in the denominator. The answer would therefore be 1001/1