证明题 紧急！！！！！！！！！！！

放缩,然后裂项:
1+1/(2^2)+1/(3^2)+1/(4^2)+……+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

这是高等数学啊！楼主几年级？
可以用面积证明

用面积证明1+1/(2^2)+1/(3^2)+1/(4^2)+……+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