一道证明不等式的高二数学题n∈N+,证明:1<1/(n+1)+1/(n+2)+1/(n+3)+……+1/(3n+1)<2

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一道证明不等式的高二数学题
n∈N+,证明:
1<1/(n+1)+1/(n+2)+1/(n+3)+……+1/(3n+1)<2

1/(n+1)>1/3n
1/(n+2)>1/3n
...
1/(n+1)+1/(n+2)+1/(n+3)+·····+1/3n +1/(3n+1)
>1/3n+1/3n+.+1/3n +1/(3n+1)
=2n/3n=2/3

你是不是打错拉