1/1*3 +1/3*5+1/5*7+1/7*9+.....+1/(99*101)
=1/2(1-1/3+1/3-1/5+1/5-1/7+.....+1/99 -1/101)
=1/2(1-1/101)
=50/101
1/3+1/15+1/35+1/63+···1/9999=?
1/1*3 +1/3*5+1/5*7+1/7*9+.....+1/(99*101)
=1/2(1-1/3+1/3-1/5+1/5-1/7+.....+1/99 -1/101)
=1/2(1-1/101)
=50/101