Giải thích các bước giải:
\(\begin{array}{l}
1,\\
{u_n} = {2^n} \Rightarrow {u_{n + 3}} = {2^{n + 3}}\\
2,\\
\left\{ \begin{array}{l}
{u_1} = 1\\
{u_{n + 1}} = n + {u_n}
\end{array} \right.,\,\,\,\left( {n \ge 1,\,\,n \in N} \right)\\
{u_{n + 1}} = n + {u_n} \Leftrightarrow {u_{n + 1}} - {u_n} = n\\
\Rightarrow \left\{ \begin{array}{l}
{u_2} - {u_1} = 1\\
{u_3} - {u_2} = 2\\
{u_4} - {u_3} = 3\\
.....\\
{u_{11}} - {u_{10}} = 10
\end{array} \right.\\
\Rightarrow \left( {{u_2} - {u_1}} \right) + \left( {{u_3} - {u_2}} \right) + \left( {{u_4} - {u_3}} \right) + .... + \left( {{u_{11}} - {u_{10}}} \right) = 1 + 2 + 3 + .... + 10\\
\Leftrightarrow {u_{11}} - {u_1} = \frac{{11.10}}{2}\\
\Leftrightarrow {u_{11}} - 1 = 55\\
\Leftrightarrow {u_{11}} = 56\\
3,\\
\left\{ \begin{array}{l}
{u_1} = 2\\
{u_{n + 1}} = {2^n}.{u_n}
\end{array} \right.\,\,\,\,\left( {n \ge 1;\,\,n \in N} \right)\\
{u_{n + 1}} = {2^n}.{u_n}\\
\Rightarrow {u_5} = {2^4}.{u_4} = {2^4}.\left( {{2^3}.{u_3}} \right) = {2^4}{.2^3}{.2^2}.{u_2} = {2^4}{.2^3}{.2^2}{.2^1}.{u_1} = {2^{10}}.{u_1} = {2^{11}}
\end{array}\)
