观察下列三组等式,①1/(1x2)=1/1-1/2,1/(2x3)=1/2-1/3,1/(3x4)=1/3-1/4；②2/(1x3)=1/1-1/3,2/(2x4)=1/2-1/4,2/(3x5)=1/3-1/5；③3/(1x4)=1/1-1/4,3/(2x5)=1/2-1/5,3/(3x6)=1/3-1/6.问：计算1/(3x6)+1/(6x9)+1/(9x12)+.+1/3nx(3n+3)问：计算1/(2^2

观察下列三组等式,①1/(1x2)=1/1-1/2,1/(2x3)=1/2-1/3,1/(3x4)=1/3-1/4；②2/(1x3)=1/1-1/3,2/(2x4)=1/2-1/4,2/(3x5)=1/3-1/5；③3/(1x4)=1/1-1/4,3/(2x5)=1/2-1/5,3/(3x6)=1/3-1/6.问：计算1/(3x6)+1/(6x9)+1/(9x12)+.+1/3nx(3n+3)问：计算1/(2^2
观察下列三组等式,
①1/(1x2)=1/1-1/2,1/(2x3)=1/2-1/3,1/(3x4)=1/3-1/4；
②2/(1x3)=1/1-1/3,2/(2x4)=1/2-1/4,2/(3x5)=1/3-1/5；
③3/(1x4)=1/1-1/4,3/(2x5)=1/2-1/5,3/(3x6)=1/3-1/6.
问：计算1/(3x6)+1/(6x9)+1/(9x12)+.+1/3nx(3n+3)
问：计算1/(2^2-1)+1/(3^2-1)+1/(4^2-1)+.+1/(9^2-1)+1/(10^2-1)

观察下列三组等式,①1/(1x2)=1/1-1/2,1/(2x3)=1/2-1/3,1/(3x4)=1/3-1/4；②2/(1x3)=1/1-1/3,2/(2x4)=1/2-1/4,2/(3x5)=1/3-1/5；③3/(1x4)=1/1-1/4,3/(2x5)=1/2-1/5,3/(3x6)=1/3-1/6.问：计算1/(3x6)+1/(6x9)+1/(9x12)+.+1/3nx(3n+3)问：计算1/(2^2
1)=1/3*(1/3-1/6+1/6-1/9+.-1/3n+3)
=1/3*(1/3-1/3n+3)
=n/(9n+9)
2)=1/[(2+1)(2-1)]+.+1/[(10+1)(10-1)]
=1/2*(1-1/3+.1/9-1/11)
=1/2*(1-1/11)
=5/11

1. 1/3*(1/3-1/6+1/6-1/9+……+1/(3n-3)-1/3n+1/3n-1/(3n+3))=1/3*(1/3-1/(3n+3))=1/9-1/(9(n+1))

2. 1/((2+1)(2-1)0+1/((3+1)(3-1))+……+1/((9+1)(9-1))+1/((10+1)(10-1))

   =1/(1*3)+1/(2*4)...

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   1. 1/3*(1/3-1/6+1/6-1/9+……+1/(3n-3)-1/3n+1/3n-1/(3n+3))=1/3*(1/3-1/(3n+3))=1/9-1/(9(n+1))

   2. 1/((2+1)(2-1)0+1/((3+1)(3-1))+……+1/((9+1)(9-1))+1/((10+1)(10-1))

      =1/(1*3)+1/(2*4)+1/(3*5)+……+1/(8*10)+1/(9*11)

      =1/2*(1-1/3+1/2-1/4+1/3-1/5+……+1/8-1/10+1/9-1/11)

      =1/2*(1+1/2-1/10-1/11)=1/2*(3/2-21/110)=3/4-21/220

      
      

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