初中一年级数学计算题:1/3+1/3×5＋1/5×7+1/7×9+…＋1/97×99＋1/99×101=?怎么计算的？

1/3+1/3×5＋1/5×7+1/7×9+…＋1/97×99＋1/99×101

=1/2[1-1/3]+1/2[1/3-1/5]+...+1/2[1/99-1/101]

=1/2[1-1/3+1/3-1/5+....+1/99-1/101]

=1/2[1-1/101]

=1/2*100/101

=50/101

1/3+1/3×5＋1/5×7+1/7×9+…＋1/97×99＋1/99×101=?

1/3=(1/2)*(1-1/3)
1/(3*5)=(1/2)*(1/3-1/5)
1/(5*7)=(1/2)*(1/5-1/7)
.......

1/3+1/3×5＋1/5×7+1/7×9+…＋1/97×99＋1/99×101
=(1/2)(1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101)
=(1/2)(1-1/101)
=(1/2)(100/101)
=50/101

应该是这样：
1/3+1/3×5＋1/5×7+1/7×9+…＋1/97×99＋1/99×101

=1/2[1-1/3]+1/2[1/3-1/5]+...+1/2[1/99-1/101]

=1/2[1-1/3+1/3-1/5+....+1/99-1/101]

=1/2[1-1/101]

=1/2*100/101

=50/101
不知道对不对！

1/3+1/3×5＋1/5×7+1/7×9+…＋1/97×99＋1/99×101
=(1/2)(1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101)
=(1/2)(1-1/101)
=(1/2)(100/101)
=50/101

1/3+1/3×5＋1/5×7+1/7×9+…＋1/97×99＋1/99×101
=1/2[1-1/3]+1/2[1/3-