求证;1+1/2+1/3+······+1/k≧(2k)/(k+1)
问题描述:
求证;1+1/2+1/3+······+1/k≧(2k)/(k+1)
用数学归纳法和柯西不等式!
答
当n=1时,左边=1,右边=1,此时不等式成立;假设当n=k时,不等式也成立,即,1+1/2+1/3+...1/k大于等于2k/k+1,那么,当n=k+1时,1+1/2+1/3+...1/k+1/(k+1)大于等于2k/k+1+1/(k+1),1+1/2+1/3+...1/k+1/(k+1)大于等于2k+1/(k+1...