Question

求解一道小学数学题

1/3+1/15+1/35+1/63+1/99=？
用最简单的方法，谢谢

Answer 1

1/3=1/2*(1/1-1/3)
1/15=1/2*(1/卖如瞎3-1/5)
每一项都这样拆开
最后等于1/中空2*(1/橡前1-1/3+1/3-1/5+....1/9-1/11)=0.5*(1-1/11)=5/11

Answer 2

1/3+1/15+1/35+1/63+1/99
=1/2(1-1/3)+1/2(1/3-1/5)+……1/2（1/9-1/11)
=1/2(1-1/3+1/稿前袜3-1/5+……键激1/9-1/11)
=1/2(1-1/11)
=5/11
不明悔租请指出

Answer 3

1/3+1/15+1/35+1/63+1/99
=1/2×(1-1/3+1/3+1/5+……＋胡笑1/9－1/11）裤衫含塌键
＝1/2×(1－1/11)
＝5/11

Answer 4

1/3+1/15+1/迹顷游35+1/63+1/99
=(1-1/3+1/3-1/5+1/5-1/乎纯7+1/7-1/9+1/9-1/11)/2
=(1-1/11)/姿销2
=5/10

Answer 5

1/3=1/(1*3);1/15=1/3*5;1/扰或橘35=1/(5*7).....
所以1/3=1/2*(1-1/3);1/15=1/团源2(1/3-1/5)...
所以=1/2(1-1/11)=5/缓团11

Answer 6

1/3+1/15+1/35+1/63+1/猜册厅99=1/2[(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/姿蔽9)+(1/9-1/11)]=1/2(1-1/穗隐11)=5/11