求证ln2/(2^4)+ln3/(3^4)+……+ln n/(n^4)

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/23 21:18:58
求证ln2/(2^4)+ln3/(3^4)+……+lnn/(n^4)求证ln2/(2^4)+ln3/(3^4)+……+lnn/(n^4)求证ln2/(2^4)+ln3/(3^4)+……+lnn/(n^

求证ln2/(2^4)+ln3/(3^4)+……+ln n/(n^4)
求证ln2/(2^4)+ln3/(3^4)+……+ln n/(n^4)

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)