Question

谁帮我解决一下这道简便计算题啊，过程答案都要有!

1/1*2*3+1/2*3*4+…+1/20*21*22

Answer 1

解题思路：1/n(n+1)(n+2)
=1/2{[(n+2)-n]/[n(n+1)(n+2)]}
=1/2[1/n(n+1)-1/(n+1)(n+2)]
所以原式=1/2[（1/1x2-1/2x3)+(1/2x3-1/3x4)+(1/3x4-1/4x5)+……+(1/20x21-1/21x22)]
=1/2(1/1x2 -1/2x3+1/2x3 -1/3x4+1/3x4 -1/4x5+……+1/20x21-1/21x22)
=1/2(1/1x2-1/21x22)
=1/2×230/462
=115/462
祝你好运

Answer 2

解题思路：1/n(n+1)(n+2)
=1/2{[(n+2)-n]/[n(n+1)(n+2)]}
=1/2[1/n(n+1)-1/(n+1)(n+2)]
所以原式=1/2[（1/1x2-1/2x3)+(1/2x3-1/3x4)+(1/3x4-1/4x5)+……+(1/20x21-1/21x22)]
=1/2(1/1x2 -1/2x3+1/2x3 -1/3x4+1/3x4 -1/4x5+……+1/20x21-1/21x22)
=1/2(1/1x2-1/21x22)
=1/2×230/462
=115/462