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试证：对任意的正整数n,有1/1*2*3+1/2*3*4+……+1/n(n+1)*(n+2)
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试证：对任意的正整数n,有1/1*2*3+1/2*3*4+……+1/n(n+1)*(n+2)
▼优质解答
答案和解析
1/1*2*3+1/2*3*4+……+1/n*(n+1)*(n+2)
=1/2*[1/1*2-1/2*3+1/2*3-1/3*4+……+1/n(n+1)-1/(n+1)*(n+2)]
=1/2*[1/1*2-1/(n+1)(n+2)]
=1/4-1/(n+1)*(n+2)
=1/2*[1/1*2-1/2*3+1/2*3-1/3*4+……+1/n(n+1)-1/(n+1)*(n+2)]
=1/2*[1/1*2-1/(n+1)(n+2)]
=1/4-1/(n+1)*(n+2)
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