原式=(1+2+...+n)/n^2
=(1+n)*n/(2n^2)
=(1+n)/(2n)
=1/(2n)+1/2
当n趋近于无穷的时候
原式=1/2
lim/n→无穷(1/n^2+2/n^2+……+n/n^2)
=lim/n→无穷[(1+2+……+n/)n^2]
=lim/n→无穷[(1+n/)2n]
=1/2
(1/n^2+2/n^2+……+n/n^2)=n(n+1)/(2n^2)=1/2*(1+1/n)
n趋向无穷,(1/n^2+2/n^2+……+n/n^2)趋向1/2
lim/x→无穷(1/n^2+2/n^2+……+n/n^2)=1/2
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lim/x->无穷(n(n+1)/2n^2)=1/2
1/2