1/2=1-1/2; 1/2×3=1/2 -1/3; 1/3x4 = 1/3 - 1/4 ; 假如截止到这里,那么中间的二分之一、三分之一都是可以约去的;也就是说约完中间的各项后只是保留了头和尾,结果是 1-1/2010 =2009/2010先约分再化简;
原式=1-1/2+1/2-1/3+1/3-1/4+…+1/n-(1/n+1)=最后都约掉了只剩下首项和尾项=
1-(1/n+1)=n/n+1
所以可知原式=1-1/2010=2009/2010
-1^4×﹛[6又2/3÷(-4)-3又3/4×(-0.4)]÷(-1/6)-4﹜
=-1*{【20/3*1/4+15/4*4/10】÷(-1/6)-4﹜
=19-4=15
1/n(n+1)=1/n-(1/n+1)
(1)1/1*2+1/2*3+…+1/n(n+1)=1-1/2+1/2-1/3+1/3-1/4+…+1/n-(1/n+1)=
1-(1/n+1)=n/n+1
(2)1/1*3+1/3*5+1/5*7+1/7*9+1/9*11=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(1-1/3+1/3+....+1/9-1/11)=1/2*10/11=5/11