设f(n)=1/n+1+1/n+2+1/n+3+……+1/3n(n∈N+),则f(n+1)-f(n)=?

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设f(n)=1/n+1+1/n+2+1/n+3+……+1/3n(n∈N+),则f(n+1)-f(n)=?

f(n+1)-f(n)=1/(3n+1) + 1/(3n+2)+ 1/(3n+3)- 1/(n+1)=1/(3n+1) + 1/(3n+2)- 2/(3n+3)>0