Question

(1)1*2+2*3+3*4+.n+(n+1) (2)1*2+2*3+3*4.9*10

Answer 1

1*2+2*3+3*4+.n*(n+1)

=1*(1+1)+2*(2+1)+3*(3+1)+.n*(n+1)

=1^2+1+2^2+2+3^2+.n^2+n

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

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

=(n+1)(2n^2+n+3n)/6

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

所以1*2+2*3+3*4.9*10

=（9+1）（9^2+2*9)/3

=10*33

=330

如有不明白,可以追问!

谢谢采纳!