Question

1/1*2*3+ 1/2*3*4+ 1/3*4*5+...+1/20+21+22简算

简便运算

Answer 1

解：
1/1*2*3=(1/1*2-1/2*3)*1/2
1/2*3*4=(1/2*3-1/3*4)*1/2
……
1/20*21*22=(1/20*21-1/21*22)*1/2

1/（1*2*3）+1/（2*3*4）+1/（3*4*5）+...+1/（20*21*22）
=(1/1*2-1/2*3)*1/2+(1/2*3-1/3*4)*1/2+.........+(1/20*21-1/21*22)*1/2
=1/2*(1/1*2-1/2*3+1/2*3-........-1/21*22)
=1/2*(1/1*2-1/21*22)
=115/462

Answer 2

=(1/2)*(1/1*2-1/2*3)+(1/2)*(1/2*3-1/3*4)+……+(1/2)*(1/20*21-1/21*22)
=(1/2)*(1/1*2-1/2*3+1/2*3-1/3*4+……+1/20*21-1/21*22)
=(1/2)*(1/1*2-1/21*22)
=115/462

Answer 3

=(1/2)*(1/1*2-1/2*3)+(1/2)*(1/2*3-1/3*4)+……+(1/2)*(1/20*21-1/21*22)
=(1/2)*(1/1*2-1/2*3+1/2*3-1/3*4+……+1/20*21-1/21*22)
=(1/2)*(1/1*2-1/21*22)
=115/462