求数学高手。。题目是初高中衔接教材上的。。
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1/1X3+1/2X4+1/3X5+······+1/(n-1)X(n+1)+1/(n(n+2)
= (1/2)(1 - 1/3) + (1/2)(1/2 - 1/4)+ (1/2)(1/3 - 1/5) + ... + (1/2)[1/(n-1)-1/(n+1)]+ (1/2)[1/n-1/(n+2)]
= (1/2)[1 - 1/3 + 1/2 - 1/4 +1/3 - 1/5 ... + 1/(n-2)-1/n+ 1/(n-1)-1/(n+1)+ 1/n-1/(n+2)
= (1/2)[(1 + 1/2 - 1/(n+1) - 1/(n+2)
= (1/2)(1 - 1/3) + (1/2)(1/2 - 1/4)+ (1/2)(1/3 - 1/5) + ... + (1/2)[1/(n-1)-1/(n+1)]+ (1/2)[1/n-1/(n+2)]
= (1/2)[1 - 1/3 + 1/2 - 1/4 +1/3 - 1/5 ... + 1/(n-2)-1/n+ 1/(n-1)-1/(n+1)+ 1/n-1/(n+2)
= (1/2)[(1 + 1/2 - 1/(n+1) - 1/(n+2)
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