1/1X3+1/3X5+…….+1/99X101
=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