Math CentralQuandaries & Queries


Question from Mrityun, a student:

can you pls answer this :

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.).


About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS