1+2+3……+2n
=(1+2n)*2n/2
=n*(1+2n)
lim[(1/n^2+1)+(2/n^2+1)+(3/n^2+1)+.+(2n/n^2+1)]lim[(1/n^2+1)+(2/n^2+1)+(3/n^2+1)+.+(2n/n^2+1)]
=limit[(2n^2+n)/(n^2+1)]
=2