在澳洲登不上战网:数学题,急急急!!!!!!!

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已知1/x(x+2)=0.5(A/x-b/x+2),求A、B的值。并利用它计算(1/1*3)+(1/2*4)+(1/3*5)+……+(1/n(n+2))

1/x(x+2)=0.5[A/x-b/(x+2)]
A=B=1
1/x(x+2)=0.5[1/x-1/(x+2)]

1/1*3)+(1/2*4)+(1/3*5)+……+(1/n(n+2))
=0.5[1-1/3+1/2-1/4+1/3-1/5+....+1/n-1/(n+2)]
=0.5[1+1/2-1/(n+1)-1/(n+2)]
=3/4-1/[2(n+1)]-1/[2(n+2)]