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## Homework Statement

Lim

n[tex]\rightarrow[/tex][tex]\infty[/tex] [tex]\sum(1+2i/n)^2(2/n)[/tex]

## Homework Equations

[tex]\sumi = n(n+1)/2[/tex]

[tex]\sumi^2 = n(n+1)(2n+1)/6[/tex]

[tex]\sum[n(n+1)/2]^2[/tex]

## The Attempt at a Solution

n[tex]\rightarrow[/tex][tex]\infty[/tex] [tex]\sum(1+2i/n)^2(2/n)[/tex]

= n[tex]\rightarrow[/tex][tex]\infty[/tex] 2/n[[tex]\sum(1+4i/n+4i^2/n^2)][/tex]

= n[tex]\rightarrow[/tex][tex]\infty[/tex] 2/n (n) (n^2) [tex]\sum1[/tex] + [tex]4\sumi[/tex] + [tex]4\sumi^2[/tex]

= n[tex]\rightarrow[/tex][tex]\infty[/tex] 2n^2 [n + 4[n(n+1)/2] + 2[n(n+1)(2n+1)/3]]

=...?