How can I use the squaring sequences theorem to show that the limit is two?

[hollow ivy]

each component u_nm (1 <= m <= 2n) of sum for u_n is bounded like

1/(n+1) < u_nm < 1/n, since n^2 + 2n + 1 > n^2 + m > n^2,

Each u_n have 2n components, so we have

2n/(n+1) < u_n < 2. Now it's obvious that we have 2 as a limit for u_n