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