1/(1×3)+1/（3×5）+1/（5×7）+1/（7×9）+...+1/（49×51）
＝(1-1/3)×1/2+（1/3-1/5）×1/2+(1/5-1/7)×1/2+(1/7-1/9)×1/2+...+（1/49-1/51）×1/2
=(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+...+1/49-1/51)×1/2
=(1-1/51)×1/2
=50/51×1/2
=25/51
是计算题我打不出题目见谅
1/(1×3)+1/（3×5）+1/（5×7）+1/（7×9）+...+1/（49×51）
＝(1-1/3)×1/2+（1/3-1/5）×1/2+(1/5-1/7)×1/2+(1/7-1/9)×1/2+...+（1/49-1/51）×1/2
=(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+...+1/49-1/51)×1/2
=(1-1/51)×1/2
=50/51×1/2
=25/51