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| Math Central | Quandaries & Queries |
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Question from Mrityun, a student: Hi suppose a,b and c are natural numbers such that 1/a + 1/b + 1/c < 1. Prove that 1/a + 1/b + 1/c < = 41/42. for the past one week I am trying to solve this. |
Maybe you should approach it as follows: What is the largest 1/a could be? 1/2. (Note you can take a = 2 for if max{1/a, 1/b, 1/c} < 1/2 the result follows easily.)
If a = 2, how large could 1/b be? 1/3. Continuing in this way you find c =7 which is 2x3+1 (and if you had 1/a + 1/b + 1/c +1/d < 1 then d = 2x3x7+1, etc.).
Penny
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