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+1/7-1/9+...+1/99-1/101)=(1/2)(1-1/101)=50/101
