1/3+1/15+1/35+.+1/9999
=1/(1×3)+1/(3×5)+1/(5×7)+…+1/(99×101)
=½(1-1/3)+½(1/3-1/5)+½(1/5-1/7)+ …+½(1/99-1/101)
=½(1-1/3+1/3-1/5+1/5-1/7+ …+1/99-1/101)
=½(1-1/101)
=½×100/101
=50/101
1/3+1/15+1/35+.+1/9999
1/3+1/15+1/35+.+1/9999
=1/(1×3)+1/(3×5)+1/(5×7)+…+1/(99×101)
=½(1-1/3)+½(1/3-1/5)+½(1/5-1/7)+ …+½(1/99-1/101)
=½(1-1/3+1/3-1/5+1/5-1/7+ …+1/99-1/101)
=½(1-1/101)
=½×100/101
=50/101