求证ln2^4/2^4+ln3^4/3^4+……+lnn^4/n^4＜2/e

题目

求证ln2^4/2^4+ln3^4/3^4+……+lnn^4/n^4＜2/e

答案

楼上看问题错啦先证明2＜x时,lnx＜x/2所以lnx^2＜x,所以(lnx^2)/x^2＜1/X所以ln2^4/2^4+ln3^4/3^4+••••••+lnn^4/n^4＜1/2^2+1/3^2+……+1/n^2＜1/4+1/9+1/(3•4)+•&...