1/1×3 + 1/3×5 + 1/5×7 +……+ 1/99×101 等于多少啊?

1/1*3=(1-1/3)/21/3*5=(1/3-1/5)/2。所以原式=[(1-1/3)+(1/3-1/5)+(1/5-1/7)+。+(1/99-1/101)]/2=(1-1/3+1/3-1/5+1/5-。+1/99-1/101)/2=(1-1/101)/2=50/101