1/(1*3)+1/(3*5)+1/(5*7)+.1/(99*101)
=(1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+.(1/99-1/101)/2
=(1-1/3+1/3-1/5+1/5-1/7+.1/99-1/101)/2
=(1-1/101)/2
=(100/101)/2
=50/101
【问题补充：请看好题目,是一乘三分之一 分数】
难道是：1*1/3+3*1/5+5*1/7+.99*1/101
=1/3+3/5+5/7+.99/101
=(1-2/3)+(1-2/5)+(1-2/7)+.(1-2/101)
=(1+1+1...共50个1) - 2 * (1/3+1/5+1/7+.1/101)
=50-2(1/3+1/5+1/7+.1/101)