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1/1X4+1/4X7+1/7X10+1/10X13+1/13X16(简算)

1/1x4+1/4x7+1/7x10+1/10x13+1/13X16 =(1/3) * [ (1-1/4) + (1/4-1/7) + (1/7-1/10) + (1/10-1/13) + (1/13-1/16) ]=(1/3) * [ 1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16 ]=(1/3) * [ 1-1/16 ]=(1/3) * (15/1

1/(1x4)+1/(4x7)+1/(7x10)+1/(10x13)=1/3x(1-1/4)+1/3x(1/4-1/7)+1/3x(1/7-1/10)+1/3x(1/10-1/13)=1/3x(1-1/4+1/4-1/7+1/7-1/10+1/10-1/13)=1/3x(1-1/13)=1/3x12/13=4/13

1/1*4+1/4*7+1/7*10+1/10*13+1/13*16=1/3*(1-1/4)+1/3*(1/4-1/7)+1/3*(1/7-1/10)+1/3*(1/10-1/13)+1/3*(1/13-1/16)=1/3*(1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16)=1/3*(1-1/16)=1/3*15/16=5/16

999

最后一项应该是16x19吧原式=1/3 x [1/4 -1/7 +1/7 -1/10 ++1/16 - 1/19]=1/3x(1/4-1/19)=1/3 x 15/76=5/76

1x4分之1+4x7分之1+7x10分之1+10x13分之1+13x16分之1 =1/3*(1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16)=1/3*(1-1/16)=1/3*15/16=5/16

这是常见的裂项求和的问题啊,是有通法的,设通项是1/n(n+r),其中r是常数,那么通项可以裂项为 1/r[1/n - 1/(n+r)],也就是两项1/n和1/(n+r)之差前面再乘个系数1/r 对于这道题,相当于r=3,通项可裂项为1/3[1/n-1/(n+3)],所以原式可化为 1/3[(1-1/4)+(1/4-1/7)+(1/7-1/10)+(1/10-1/13)+(1/13-1/16)]=1/3(1-1/16)=5/16

原式=1/3(1-1/4)+1/3(1/4-1/7)+…+1/3(1/13-1/16)=1/3[1-1/4+1/4-1/7+…+1/13-1/16]=1/3*15/16=5/16

原式=(1-1/4+1/4-1/7)+1/7-1/10+1/10-1/13)x1/3=(1-1/13)x1/3=12/13x1/3=4/13 请好评 ~在右上角点击【评价】,然后就可以选择【满意,问题已经完美解决】了.如果你认可我的回答,敬请及时采纳,~你的采纳是我前进的动力~~ ~如还有新的问题,请不要追问的形式发送,另外发问题并向我求助或在追问处发送问题链接地址,答题不易,敬请谅解~~ O(∩_∩)O,记得好评和采纳,互相帮助 祝学习进步!

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