7th CanMO 1975 Problem Evaluate (1·2·4 + 2·4·8 + 3·6·12 + 4·8·16 + ... + n·2n·4n) 1/3 /(1·3·9 + 2·6·18 + 3·9·27 + 4·12·36 + ... + n·3n·9n) 1/3 .
The numerator cubed is 8(1 3 + 2 3 + ... + n 3 ), the denominator cubed is 27(1 3 + 2 3 + ... + n 3 ). Hence the expression is 2/3. 7th CanMO 1975 © John Scholes jscholes@kalva.demon.co.uk 10 June 2002