Question

求数列1+3+6+10+15+21+28+36的和

Answer 1

1+3+6+10+15+21+28+36

=1/2*1*2+1/2*2*3+1/2*3*4+...+1/2*8*9

=1/2[1*2+2*3+3*4+...+8*9]

=1/2[1/3*1*2*3+1/3*(2*3*4-1*2*3)+1/3(3*4*5-2*3*4)+...+1/3(8*9*10-7*8*9)]

=1/6(1*2*3+2*3*4-1*2*3+3*4*5-2*3*4+...+8*9*10-7*8*9)

=1/6*8*9*10

=120

公式：1*2+2*3+3*4+...+n(n+1)=1/3n(n+1)(n+2)