1樓:匿名使用者
原式=(1+1/2+1/3+1/4+1/5)x(1/2+1/3+1/4+l/5+1/6-1/2-1/3-1/4-1/5-1/6)
=(1+1/2+1/3+1/4+1/5)x0=o
(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/6)-(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4)簡便運算 過程
2樓:匿名使用者
(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)
所以:(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/6)-(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+1/6)-[(1+1/2+1/3+1/4)*(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+1/6)-(1+1/2+1/3+1/4)*(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+1/6-(1/2+1/3+1/4)]-(1/5)*(1/2+1/3+1/4)
=(1+1/2+1/3+1/4)*(1/6)-(1/5)*(1/2+1/3+1/4)
再把前一項這個搞一次咯。
簡便運算:(1/2+1/3+1/4+1/5)*(1/3+1/4+1/5+1/6)-(1/2+1/3+1/4+1/5+1/6)+(1/3+1/4+1/5)
3樓:盍玉枝之丙
似乎沒有特bai別du簡便的方zhi
法:前一部分通dao分回
(1/2+1/3+1/4+1/5)*(1/3+1/4+1/5+1/6)-(1/2+1/3+1/4+1/5+1/6)+(1/3+1/4+1/5)
=(30/60+20/60+15/60+12/60)*(20/60+15/60+12/60+10/60)-[(1/2+1/3+1/4+1/5+1/6)-(1/3+1/4+1/5)]
=77/57-[(1/2+1/6)]
=77/57-2/3
=(77-2×19)答/57
=13/19
4樓:有竹菅媼
用數列算呀:(1/2+1/3+1/4+1/5)*(1/3+1/4+1/5+1/6)-(1/2+1/3+1/4+1/5+1/6)+(1/3+1/4+1/5)這可以分四項用等差公式sn
=n[a1+an
]/2很間單的
(1/2+1/3+1/4+1/5)*(1/3+1/4+1/5+1/6)-(1/2+1/3+1/4+1/5+1/6)*(1/3+1/4+1/5) 要簡便運算 5
5樓:匿名使用者
你好設+1/3+1/4+1/5=a,則
(1/2+a)(a+1/6)-(1/2+a+1/6)*a=1/2a+a2 +1/12+1/6a-(1/2a-a2 +1/6a)
=1/12
如果本題有什麼不明白可以追問,如果滿意記得採納祝學習進步!
6樓:匿名使用者
想1/2+1/3+1/4+1/5為a,1/3+1/4+1/5為b,可寫成
a*(b+1/6)-(a+1/6)*b
=(ab+1/6a)-(ab+1/6b)
=ab+1/6a-ab-1/6b
=1/6a-1/6b
=(1/2+1/3+1/4+1/5)*1/6-(1/3+1/4+1/5)*1/6
=(1/2+1/3+1/4+1/5-1/3-1/4-1/5)*1/6=1/12
7樓:匿名使用者
設a=1/2+1/3+1/4+1/5 b=1/3+1/4+1/5+1/6
則 原式=ab-(a+1/6)*(b-1/6)=1/6 (a-b+1/6)
=1/6 (1/2-1/6+1/6)
=1/12
8樓:血匙
=(1/2+1/3+1/4+1/5)*1/6-1/6*(1/3+1/4+1/5)=1/2*1/6=1/12
(1/2+1/3+1/4)×(1/3+1/4+1/5)-(1/2+1/3+1/4+1/5)×(1/3+1/4)進行簡便運算還要過程和答案
9樓:匿名使用者
設:1/2+1/3+1/4=a 1/3+1/4=b a-b=1/2
a×(b+1/5)-(a+1/5)×b
=ab+1/5a-ab-1/5b
=1/5(a-b)
=1/5×1/2
=1/10
10樓:匿名使用者
令1/3+1/4=a則原式
=(1/2+a)(a+1/5)-(1/2+a+1/5)a=a2+a/2+a/5+1/10-a2-a/2-a/5=1/10
11樓:藍染_煙影
原式=(1/2+1/3+1/4)*(1/3+1/4)+(1/2+1/3+1/4)*1/5-(1/2+1/3+1/4)*(1/3+1/4)-1/5*(1/3+1/4)
=(1/2+1/3+1/4)*1/5-1/5*(1/3+1/4)=1/2*1/5+(1/3+1/4)*1/5-1/5*(1/3+1/4)
=1/2*1/5
=1/10
1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7 簡便運算怎麼算?請詳細分解運算過程,謝謝
12樓:暖光小圖
1/m(m+1)=1/m-1/(m+1)
原式zhi
dao=(1/1-1/2)+(
版1/2-1/3)
權+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7
13樓:¢不二月嵐
1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7
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