(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)—(1+1/2+1/3+1/4+1/5)×(1/2+1/3+1/4)
来源:百度知道 编辑:UC知道 时间:2024/06/07 12:44:57
如题!简便方法 每一步的过程 有原理更好!!!!!!!!!!!
你发现没有你把 1/2+1/3+1/4设成=a 那么题就变成
(1+a)*(a+1/5)-(1+a+1/5)*a
=a+1/5+a*(a+1/5)-a-a*(a+1/5)
看到这步就明白了吧?
结果=1/5
其实做这些题你要找共同点,能用一个东西代替式子里的大部分东西就可以用代替法试试,说不定还能得到意外的结果!
(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)—(1+1/2+1/3+1/4+1/5)×(1/2+1/3+1/4+1/5-1/5)
=(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)—(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-1/5×(1/2+1/3+1/4+1/5)+1/5×(1+1/2+1/3+1/4)+1/5×1/5
=-1/5×(1/2+1/3+1/4+1/5-(1+1/2+1/3+1/4)-1/5)
=1/5
{1+1/2+1/3+1/4}*{1/2+1/3+1/4+1/5}-{1+1/2+1/3+1/4+1/5}*{1/2+1/3+1/4}
={1+1/2+1/3+1/4}*{1/2+1/3+1/4+1/5}-{1/2+1/3+1/4+1/5}* {1/2+1/3+1/4}-{1/2+1/3+1/4}
={1/2+1/3+1/4+1/5}-{1/2+1/3+1/4}
=1/5
设1/2+1/3+1/4=t
原式=(1+t)(t+1/5)-t(t+1+1/5)=1/5
(1/2005-1)(1/2004-1)........(1/3-1)(1/2-1)
1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+100)
1+1/(1+2)+1/(1+2+3)+-------+1/(1+2+3+----+100)
1+1/2+1/3+.....+1/n
1+1/2+1/3+...+1/100
1-1/2+1/3-.....-1/10
(1+1/2+1/3+1/4)×
(1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/1000)
1+1/1+2+1/1+2+3+...+1/1+2+3...+2000
1*(1/1+2)*(1/1+2+3)*~~~*(1/1+2+~~~2005)=?