1/1+1/3+1/7+1/15+.+1/2^n-1
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1/1+1/3+1/7+1/15+.+1/2^n-1
1/1+1/3+1/7+1/15+.+1/2^n-1
1/1+1/3+1/7+1/15+.+1/2^n-1
证明:
当n>1时,显然有:[2^n] - [2^(n-1)] = [2^(n-1)] >1
即:[2^n] - 1 > [2^(n-1)]
进一步:1/ (2^n - 1)
原式<1+1/(1*2)+1/(2*3)+1/(3*4)+……+1/(n-1)n
=1+1-1/2+1/2-1/3+……+1/(n+1)-1/n
=2-1/n<2