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1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7 怎样简便运算

=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

=1-1/2+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 =1-1/9 =8/9

1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10 =1-1/2+1/2-1/3+1/3-....-1/9+1/9-1/10 =1-1/10 =9/10

因为an=n*(n-1)/n+1 所以每个数可以看成2/3+(1+2/4)+(2+2/5)+(3+2/6)...+(8+2/11)= 1+2+3...+8+2/3+2/4+2/5...+2/11=36+2*(1/3+1/4+1/5+...1/11) 因为后面的那个是一个发散数列,好像没有求和公式,所以只能同分计算,当然可以把简单...

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

先求它们的倒数和,再把结果倒回来。 1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9+9x10+10x11 =10×(10+1)×(10+2)÷3 =10×11×12÷3 =110×12÷3 =1320÷3 =440

n=10 ,很好算得,得440。也许我的方法很麻烦,但是思路是很不错的,可以1x2 2x3 3x4 4x5 5x6 6x7 7x8 8x9 9x10 10x11 =2 6 12 20

你在算算 是210个6

1x2 + 2x3 + 3x4 + ...... + n(n+1) = 1/3 * n(n+1)(n+2) 1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9 = 1/3 * 8 * 9 * 10 = 240

=1/2 * ( 1/5*6-1/6*7 + 1/6*7-1/7*8 + 1/7*8-1/8*9 ) =1/2 * ( 1/5*6-1/8*9) =1/2 * 7/360 =7/720 1/a-1/b=(b-a)/ab,反之,(b-a)/ab=1/a-1/b 1/ac-1/bc=(b-a)/abc

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