1 + 2 + 3 + 4 + ... + n = 820
n + ( n - 1 ) + ( n - 2 ) + ( n - 3 ) +... + 1 = 820
= ( n + 1 ) + ( n + 1 ) + ( n + 1 ) + ... + ( n + 1 ) = 820 + 820
=> n ( n + 1 ) = 820 x 2
=> n2 + n + 1 = 1641
=> n2 + n/2 + n/2 + 1/4 + 3/4 = 1641
=> ( n + 1/2 )2 = 1641 - 3/4 = 6561/4 = ( 81/2 )2
=> n + 1/2 = 81/2
=> n = 81/2 - 1/2
=> n = 40