谁知道1/(a-1)(a+1)+1/(a +1)(a+3)+1/(a+3)(a+5)+.+1/(a +9)(a+11)=?怎样做,

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谁知道1/(a-1)(a+1)+1/(a +1)(a+3)+1/(a+3)(a+5)+.+1/(a +9)(a+11)=?怎样做,

谁知道1/(a-1)(a+1)+1/(a +1)(a+3)+1/(a+3)(a+5)+.+1/(a +9)(a+11)=?怎样做,
谁知道1/(a-1)(a+1)+1/(a +1)(a+3)+1/(a+3)(a+5)+.+1/(a +9)(a+11)=?怎样做,

谁知道1/(a-1)(a+1)+1/(a +1)(a+3)+1/(a+3)(a+5)+.+1/(a +9)(a+11)=?怎样做,
=1/2*(1/(1-a)-1/(1+a))+1/2*(1/(1+a)-1/(1+3))+.+1/2*(1/(a+9)-1/(a+11))
=1/2*(1/(1-a))-1/2*(1/(a+11))
=6/(a-1)(a+11)

[1/(a-1) - 1/(a+1) + 1/(a+1) - 1/(a+3) + ...... + 1/(a+9) - 1/(a+11)]/2
=[1/(a-1) - 1/(a+11)]/2
=5/(a-1)(a+11)