1乘以三分之一加上3乘以五分之一加上5乘以七分之一加上.....加上99乘以一百零一分之一等于多少

=（1/2）[2/1*3+2/3*5+2/5*7+2/7*9+……+2/97*99+2/99*101]
=（1/2）[(3-1)/1*3+(5-3)/3*5+(7-5)/5*7+……+（99-97）/97*99+（101-99）/99*101]
=（1/2）[1-1/3+1/3-1/5+1/5-1/7+……-1/97+1/97-1/99+1/99-1/101]
=（1/2）[1-1/101]
=50/101.

(1/1x1/3)+(1/3x1/5)+(1/5x1/7)……+(1/99x1/101)=1/2(1/1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)……+1/2(1/99-1/101)=1/2(1/1-1/3+1/3-1/5+1/5-1/7+……+1/99-1/101)=1/2(1/1-1/101)=50/101

等于1