用均值不等式证明~求证:1+1/4+1/9+1/16……+1/(n^2)<2(n∈N+)

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用均值不等式证明~求证:1+1/4+1/9+1/16……+1/(n^2)<2(n∈N+)用均值不等式证明~求证:1+1/4+1/9+1/16……+1/(n^2)<2(n∈N+)用均值不等式证明~求证:

用均值不等式证明~求证:1+1/4+1/9+1/16……+1/(n^2)<2(n∈N+)
用均值不等式证明~
求证:
1+1/4+1/9+1/16……+1/(n^2)<2(n∈N+)

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