1/2*3+1/3*4+1/4*5……+1/48*49+1/49*50是多少

1/2*3+1/3*4+1/4*5……+1/48*49+1/49*50是多少
1/2*3+1/3*4+1/4*5……+1/48*49+1/49*50是多少

1/2*3+1/3*4+1/4*5……+1/48*49+1/49*50是多少
1/2*3+1/3*4+1/4*5……+1/48*49+1/49*50
=(1/2)-(1/3)+(1/3)-(1/4)+(1/4)-(1/5)+...+(1/49)-(1/50)
=(1/2)-(1/50)
=24/50
=12/25.

上式=1/2-1/3+1/3-1/4……+1/49-1/50
=1/2-1/50
=49/100

1/2*3+1/3*4+1/4*5……+1/48*49+1/49*50
=(1/2-1/3)+(1/3-1/4)+……+(1/49-1/50)
中间抵消
=1/2-1/50
=12/25

原式=1/2-1/3+1/3-1/4........+1/49-1/50=1/2-1/50=12/25

=1/2-/1/3+1/3-1/4+...+1/49-1/50
=1/2-1/50
=49/100