1/123+1/234+1/345~1/484950=?

来源：学生作业帮助网编辑：作业帮时间：2024/05/05 02:02:13

1/1*2*3+1/2*3*4+1/3*4*5~1/48*49*50=?
1/1*2*3+1/2*3*4+1/3*4*5~1/48*49*50=?

1/1*2*3+1/2*3*4+1/3*4*5~1/48*49*50=?
1/1*2*3+1/2*3*4+1/3*4*5+.+1/48*49*50
=（1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+……+1/48*19-1/49*50）÷2
=（1/1*2-1/49*50）÷2
=（1/2-1/2450）÷2
=1/4-1/4900
=1224/4900
=306/1225

1/1*2*3+1/2*3*4+1/3*4*5~~~~~~~~1/48*49*50
=1/2*(1/1*2-1/2*3)+1/2*(1/2*3-1/3*4)+1/2*(1/3*4-1/4*5)+...+1/2*(1/48*49-1/49*50)
=1/2*(1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+...+1/48*49-1/49*50)
=1/2*(1/2-1/2450)
=1224/4900
=306/1225

1/1*2*3
=1/2×2/1*2*3
=1/2×(3-1)/1*2*3
=1/2×(3/1*2*3-1/1*2*3)
=1/2×(1/1*2-/2*3)

1+2+3+4+1 1 2 3 4 1 2 3 4 1 2 3 4 1,2,3,4, 1 2 3 4 1 2 3 4 1,2,3,4, 1,2,3,4, 1,2,3,4, 1,2,3,4, 1 2 3 4 1,2,3,4, 1,2,3,4, 1,2,3,4, 1、2、3、4 1+2+3×4 1,2,3,4