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