Question

1乘2加2乘3加3乘4一直到11乘12,得多少?1乘2加2乘3加3乘4一直到加n+1的公式

Answer 1

n(n+1)=n^2+n

1*2+2*3+3*4+…+n(n+1)

=(1^2+1)+(2^2+2)+(3^2+3)+…+(n^2+n)

=(1^2+2^2+3^2+…+n^2)+(1+2+3+…+n)

=n(n+1)(2n+1)/6+n(n+1)/2

=n(n+1)(n+2)/3

1*2+2*3+3*4+…+11*12

=11*12*13/3

=572