1/1*3+1/3*5+.+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)
=50/101