\(\left(n+1\right)u_{n+1}=n.u_n+n\)
\(\Leftrightarrow\left(n+1\right)u_{n+1}-\dfrac{1}{2}\left(n+1\right)^2+\dfrac{1}{2}\left(n+1\right)=n.u_n-\dfrac{1}{2}n^2+\dfrac{1}{2}n\)
Đặt \(n.u_n-\dfrac{1}{2}n^2+\dfrac{1}{2}n=v_n\Rightarrow\left\{{}\begin{matrix}v_1=1.u_1-\dfrac{1}{2}+\dfrac{1}{2}=0\\v_{n+1}=v_n=...=v_1=0\end{matrix}\right.\)
\(\Rightarrow n.u_n-\dfrac{1}{2}n^2+\dfrac{1}{2}n=0\)
\(\Rightarrow u_n=\dfrac{n-1}{2}\)
\(\Rightarrow u_{11}=5\)
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