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1/5*1/6+1/6*1/7+1/7*1/8+1/8*1/9+1/9*1/10=1/10...

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裂项法 1/5×1/6+1/6×1/7+1/8×1/9+1/9×1/10 =1/5-1/6+1/6-1/7+1/8-1/9+1/9-1/10 =1/5-1/10 =1/10

结果为(即第一步的结果,第二步的结果依次类推)1/2,3/5,2/3,5/7,3/4,7/9…… 发现规律 1/2,2/3,3/4,的分子分母加1。 3/5,5/7,7/9,的分子分母加2。 加到1/45时,一共出现7个结果,即是奇数个结果,那么应该是1/2,2/3,3/4,4/5中的4/...

(1/5+1/6)-(1/6-1/7)-(1/7-1/8)-(1/8-1/9) =1/5+1/6-1/6+1/7-1/7+1/8-1/8+1/9 =1/5+1/9 =9/45+5/45 =14/45

1/[n(n+1)(n+2)]=1/2*[1/n-2/(n+1)+1/(n+2)], 例如 ∴1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+1/(4*5*6)+1/(5*6*7)+1/(6*7*8)+1/(7*8*9) =1/2*[1-2/2+1/3+1/2-2/3+1/4+1/3-2/4+1/5+……+1/7-2/8+1/9] =1/2[1-1/2-1/8+1/9] =1/2(1/2-1/72) =35/144. 后面加一...

1-1/2-1/3+1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/7+1/7+1/8-1/8-1/9+1/9+1/10-1/10 =1-1/2 =1/2

看题有没有公共分式,。1有,先提取公共分式,这题一看没有公共分式,可它暗中有1/7公共分式 =1/7X5X6+1/7X6X8+1/7X8X9=1/7(5X6+6X8+8X9)=1/7X150=150/7

1/5×1/6=1/5-1/6, 1/6×1/7=1/6-1/7, 1/7×1/8=1/7-1/8, 1/8×1/9=1/8-1/9 1/9×1/10=1/9-1/10 1/5×1/6+1/6×1/7+1/7×1/8+1/8×1/9+1/9×1/10 =1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10 =1/5-1/10 =2/10-1/10 =1/10 类似的题有: 写出以下式子的...

=(5*7*4*9+5*7*8*3+5*7*2*9+7*8*9+5*7*4*3+5*8*9+5*7*9+5*7*8+7*4*9)/5*7*8*9 ={5*7*(36+24+18+12+9+8)+7*9*(8+4)+5*8*9}/5*7*8*9 =(35*107+63*12+40*9)/5*7*8*9 =3745+756+360/2520 =4861/2520 =(1260+840+630+504+420+360+315+280+252)/5*7*8*...

1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6+1/5*6*7+1/6*7*8+1/7*8*9+1/8*9*10+1/9*10*11 =(1/2)[(1/1*2)-(1/2*3)]+(1/2)[(1/2*3)-(1/3*4)]+(1/2)[(1/3*4)-(1/4*5)]+...+(1/2)[(1/9*10)-(1/10*11)] =(1/2)[(1/1*2)-(1/2*3)+(1/2*3)-(1/3*4)+(1/3*4)-(1/4*...

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