用均值不等式证明~求证:1+1/4+1/9+1/16……+1/(n^2)<2(n∈N+)
问题描述:
用均值不等式证明~
求证:
1+1/4+1/9+1/16……+1/(n^2)<2(n∈N+)
答
1+1/4+1/9+1/16+……+1/(n^2)
=1+(1-1/2)+(1/2-1/3)+(1/3-1/4)+……[1/(n-1)-1/n]
=2-1/n证毕
经典证法啊!