Question

1乘2加2乘3加3乘4，一直加到n乘(n+1) 要过程 和解释嗯

Answer 1

1乘2加2乘3加3乘4，一直加到n乘(n+1)
=2乘2加3乘3加4乘4，一直加到(n+1)乘(n+1)-[2+3+4+ (n+1)]
=(n+1)(n+2)(2n+3)/6-1)-[2+3+4+ (n+1)]
=(n+1)(n+2)(2n+3)/6-(n+1)(n+2)/2
=(n+1)(n+2)2n
=2n(n+1)(n+2)

Answer 2

an=n(n+1)=n²+n
所以Sn=(1²+2²+……+n²)+(1+2+……+n)
=n(n+1)(2n+1)/6+n(n+1)/2
=n(n+1)(n+2)/3

Answer 3

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

Answer 4

1*2+2*3+3*4+……+n(n+1)
=1^2+2^2+……+n^2+1+2+3+……+n
=n(n+1)(2n+1)/6+n(n+1)/2
=n(n+1)(n+2)/3

追问

我去查了 还有一种答案是1/2*n*（1+n)+1/6*n(n+1)(2n+1)

追答

嗯 对 看倒数第二步 你说的这个答案化简后就是我写的那个答案了