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1/2+1/6+1/12+1/20+···+1/n(n+1)的值为（）,其中n为自然数
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1/2+1/6+1/12+1/20+···+1/n(n+1)的值为（）,其中n为自然数
▼优质解答
答案和解析
1/2+1/6+1/12+1/20+...+1/n(n+1)
=(1-1/2) + (1/2-1/3) + (1/3-1/4) + (1/4-1/5) +...+ (1/n-1/(n+1))
=1-1/(n+1)
=n/(n+1)
=(1-1/2) + (1/2-1/3) + (1/3-1/4) + (1/4-1/5) +...+ (1/n-1/(n+1))
=1-1/(n+1)
=n/(n+1)
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