MathDB

4

Part of 2012 Argentina National Olympiad

Problems(1)

sum -1/a_b_i where a_i, b_i are min and max perfect square <= or >= i resp

Source: 2012 Argentina OMA Finals L3 p4

1/15/2023
For each natural number nn we denote ana_n as the greatest perfect square less than or equal to nn and bnb_n as the least perfect square greater than nn. For example a9=32a_9=3^2, b9=42b_9=4^2 and a20=42a_{20}=4^2, b20=52b_{20}=5^2. Calculate: 1a1b1+1a2b2+1a3b3+…+1a600b600\frac{1}{a_1b_1}+\frac{1}{a_2b_2}+\frac{1}{a_3b_3}+\ldots +\frac{1}{a_{600}b_{600}}
number theoryPerfect Square