计算1/2+(1/4+2/4+3/4)+(1/6+/2/6+3/6+4/6+5/6)+``````+(1/2010+2/2012+`````2009/2010)

问题描述:

计算1/2+(1/4+2/4+3/4)+(1/6+/2/6+3/6+4/6+5/6)+``````+(1/2010+2/2012+`````2009/2010)

=1/2+(1+1/2)+(2+1/2)```````+(1004+1/2)=(1+2+````+1004)+502=(1+1004)/2x1004+502剩下的你会的吧

1/2+(1/4+2/4+3/4)+(1/6+/2/6+3/6+4/6+5/6)+``````+(1/2010+2/2012+`````2009/2010)
=1/2(1+3+5+..........2009)
=1/2(1+2009)(1005)/2
=(2010)(1005)/4
=1010025/2

1/2+(1/4+2/4+3/4)+(1/6+/2/6+3/6+4/6+5/6)+``````+(1/2010+2/2010+`````2009/2010)
=1/2×(2010÷2)+(1+2+3+``````2010÷2)
=1005/2+(1+1005)×1005÷2
=1012035/2

=1/2+3/2+5/2+……+(1+2009)*(2009)/(2010*2)
=1/2+3/2+5/2+2009/2
=1/2*(1+2009)*1005/2
=505012.5

通项an=(1+2+3+……+2n-1)/(2n)=[(2n-1)(1+2n-1)/2]/(2n)=(2n-1)/2=n-(1/2)a1=1/2,a(n+1)-an=1{an}是首项为1/2,公差为1的等差数列所求的式子是{an}的前1005项的和记为S1005=1005*(1/2+1005-1/2)/2=1005*1005/2=50501...

1/2+(1/4+2/4+3/4)+(1/6+/2/6+3/6+4/6+5/6)+``````+(1/2010+2/2012+`````2009/2010)
=1/2+3/2+5/2+……+2009/2
=1005×1005/2
=505012.5