1*2*3+2*3*4+.n(n+1)(n+2)怎么解?

1*2*3+2*3*4+.n(n+1)(n+2)怎么解?
1*2*3+2*3*4+.n(n+1)(n+2)怎么解?

1*2*3+2*3*4+.n(n+1)(n+2)怎么解?
n(N+2)=n^2+2n=(n+1)^2-1
n(n+1)(n+2)=(n+1)^3-(n+1）
原式即为2^3+3^3+4^3+……+(n+1)^3-(2+3+4+……+(n+1))
=1^3+2^3+3^3+……+(n+1)^3-(1+2+3+……+(n+1))
=[(n+1)(n+2)/2]^2-(n+1)(n+2)/2