1/3+1/15+1/35+1/63+1/99+.+1/9999=?

1/3+1/15+1/35+1/63+1/99+.+1/9999=?
1/3+1/15+1/35+1/63+1/99+.+1/9999=?

1/3+1/15+1/35+1/63+1/99+.+1/9999=?
1/3+1/15+1/35+1/63+1/99+……+1/9999
=1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+1/(9×11)+……+1/(99×101)
=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+1/2(1/7-1/9)+1/2(1/9-1/11)+……+1/2(1/99-1/101)
=1/2(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+……+1/99-1/101)
=1/2(1-1/101)
=1/2×(100/101)
=50/101
很高兴为您解答,【the 1900】团队为您答题.
请点击下面的【选为满意回答】按钮.

1/3+1/15+1/35+1/63+1/99+....+1/9999
=1/(1X3)+1/(3X5)+1/(5X7)+1/(7X9)+1/(9X11)+.....+1/(99X101)
=(1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+(1/7-1/9)/2+.....+(1/99-1/101)/2
=(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+......+1/99-1/101)/2
=(1-1/101)/2
=(100/101)/2
=50/101

原式=1/3+1/2（1/3-1/9999）
=1/3+1666/9999
=4999/9999

　　1/3+1/15+1/35+1/63+1/99+....+1/9999
　　=[1－1／3＋1／3－1／5＋1／5－1／7＋1／7－1／9＋1／9－1／11＋···＋1／99－1／101]／2
　　=[1－1／101]／2
　　＝50／101

数理答疑团为你解答，希望对你有所帮助。

1/3+1/15+1/35+1/63+1/99+....+1/9999
=(1- 1/3)/2 + (1/3- 1/5)/2 + (1/5- 1/7)/2 + ...
剩下自己算

祝你学习进步，更上一层楼！ (*^__^*)