1/1+2+1/1+2+3+1/1+2+3+4+省略号+1/1+2+省略号+99
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![1/1+2+1/1+2+3+1/1+2+3+4+省略号+1/1+2+省略号+99](/uploads/image/z/3730180-4-0.jpg?t=1%2F1%2B2%2B1%2F1%2B2%2B3%2B1%2F1%2B2%2B3%2B4%2B%E7%9C%81%E7%95%A5%E5%8F%B7%2B1%2F1%2B2%2B%E7%9C%81%E7%95%A5%E5%8F%B7%2B99)
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1/1+2+1/1+2+3+1/1+2+3+4+省略号+1/1+2+省略号+99
1/1+2+1/1+2+3+1/1+2+3+4+省略号+1/1+2+省略号+99
1/1+2+1/1+2+3+1/1+2+3+4+省略号+1/1+2+省略号+99
1+2+3+.+n=n(n+1)/2
1/(1+2+3+.+n)=2/[n(n+1)]=2[1/n-1/(n+1)]
所以,上式变为
2/[1/2-1/3+1/3-1/4+.+1/99-1/100]
=2/(1/2-1/100)
=1-1/50
=0.98
99