Question

Tìm số tự nhiên n biết rằng 

1+2+3+4+...…..+n =820

Answer 1

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