证明1/(n+1)+1/(n+2)+1/(n+3)+……+1/(3n+1)>1(N属于正整数)
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令f(n)=1/(n+1)+1/(n+2)+1/(n+3)+.+1/(3n+1)

f(n+1)-f(n)=1/(3n+2)+1/(3n+3)+1/(3n+4)-1/(n+1)

=2/(3n+2)(3n+3)(3n+4)>0

f(n)递增

所以f(n)最小值为f(1)=13/12

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