1\3+1\15+1\35+1\63+1\99
来源:百度知道 编辑:UC知道 时间:2024/09/24 00:18:10
您好!
1/3+1/15+1/35+1/63+1/99
=[(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)]÷(3-1)
=[1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11]÷2
=(1-1/11)÷2
=5/11
裂项分拆:
1/(a×b)=(1/a-1/b)÷(b-a)
原式=(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
=(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11) ×1/2
=10/11×1/2=5/11
1\3+1\15+1\35+1\63+1\99
=1\(1*3)+1\(3*5)+1\(5*7)+1\(7*9)+1\(9*11)
=(1-1\3+1\3-1\5+1\5-1\7+1\7-1\9+1\9-1\11)\2
=5\11
(1+1\2)*(1+1\3)*(1+1\3)*(1+1\4)*......(1+1\20)
(1-1\2004)(1-1\2003)(1-1\2002).........(1-1\3)(1-1\2)
(1\2+1\3+...+1\2006)(1+1\2+1\3+...+1\2005)-(1+1\2+1\3+...+1\2006)(1\2+1\3+...+1\2005)
((1+1\2)(1+1\3)(1+1\4)(1+1\5)------(1+1\100))\(1-1\2)(1-1\3)(1-1\4)------(1-1\100)
((1+1\2)(1+1\3)(1+1\4)(1+1\5)------(1+1\100))\(1-1\2)(1-1\3)(1-1\4)------(1-1\100)等多少
3\1 3\1 3\1 3\1 3\1 =9\2
1*3\1+3*5\1+5*7\1+......+97*99\1
(1-1\2)+(1\2-1\3)+(1\3-1\4)+(1\4-1\5)+(1\5-1\6)+........(1\2005-1\2006
(1-1\2)+(1\2-1\3)+(1\3-1\4)+(1\4-1\5)+(1\5-1\6)+........(1\2005-1\20把括号变为绝对号咋么做06
[1+(-1\2)]+[1\2+(-1\3)]+[1\3+(-1\4)]+......[1\1999+(-1\2000)]