Each of P, Q, R, S and T are positive integers with P < Q < R < S < T. Determine the maximum value of the following expression.

[P, Q] ^-1 + [Q, R] ^-1 + [R, S] ^-1 + [S, T] ^-1

Note: [x, y] represents the LCM of x and y.

The maximum value is where each positive integer, P, Q, R, S, and T, is a power of 2.

[2⁰, 2¹]^-1 = 1/2
[2¹, 2²]^-1 = 1/4
[2², 2³]^-1 = 1/8
[2³, 2⁴]^-1 = 1/16

1/2 + 1/4 + 1/8 + 1/16 = 15/16

Posted by Dej Mar on 2008-10-03 21:22:54