23rd Swedish 1983 Problem 1 The positive integers are grouped as follows: 1, 2+3, 4+5+6, 7+8+9+10, ... Find the value of the nth sum.
The first n-1 groups have 1 + 2 + ... + n-1 = ½n(n-1) terms, so the first term of the nth group is ½n(n- 1)+1 and the last is ½n(n+1). It is an arithmetic progression with n terms, so its sum is ½n(n 2 +1). Thanks to Suat Namli 23rd Swedish 1983 © John Scholes jscholes@kalva.demon.co.uk 27 February 2004 Last corrected/updated 27 Feb 04