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