求证ln2/(2^4)+ln3/(3^4)+……+ln n/(n^4)

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求证ln2/(2^4)+ln3/(3^4)+……+ln n/(n^4)

ln2/(2^4)+ln3/(3^4)+……+ln n/(n^4)=ln2^-3+ln3^-3+…+lnn^-3=-3(in2+ln3+ln4+…+lnn)=-3lnn!
显然lnn!>ln1=0 所以-3lnn!0 所以ln2/(2^4)+ln3/(3^4)+……+ln n/(n^4)