Question

求证In2/(2^ 3)+In3/(3^ 3)+In4/(4^ 3)+.+Inn/(n^ 3)>1/e

Answer 1

左边=ln[2*3*...*n/(2^3)*(3^3)*.*(n^n)]=ln(n!)-ln(n!)^3=ln(n!)-3ln(n!)=-2ln(n!) 三种情况讨论

n>=3 左边