Đáp án:
\[{u_{10}} = 45,0333\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
{u_{n + 1}} = \sqrt {{u_n}^2 + 1} \\
\Leftrightarrow u_{n + 1}^2 = {u_n}^2 + 1\\
\Rightarrow \left\{ \begin{array}{l}
u_2^2 = u_1^2 + 1\\
u_3^2 = u_2^2 + 1\\
u_4^2 = u_3^2 + 1\\
.....\\
u_n^2 = u_{n - 1}^2 + 1
\end{array} \right.\\
\Rightarrow u_2^2 + u_3^2 + u_4^2 + .... + u_n^2 = \left( {u_1^2 + u_2^2 + u_3^2 + .... + u_{n - 1}^2} \right) + 1.\left( {n - 1} \right)\\
\Leftrightarrow u_n^2 = u_1^2 + \left( {n - 1} \right) = n + 2018\\
\Rightarrow u_{10}^2 = 10 + 2018 = 2028 \Rightarrow {u_{10}} = 45,0333
\end{array}\)
