回復 14# arend 的帖子
填充2.
有一數列\(\langle\;a_n\rangle\;\)，若\(a_1=0\)，且\(a_{n+1}-1=a_n+2\sqrt{1+a_n}\)，\(n=1,2,3,\ldots\)，求\(a_{30}=\) 。
[解答]
\(\begin{align}
& {{a}_{n+1}}-1=a{}_{n}+2\sqrt{1+{{a}_{n}}} \\
& {{a}_{n+1}}+1=a{}_{n}+1+2\sqrt{1+{{a}_{n}}}+1={{\left( \sqrt{a{}_{n}+1}+1 \right)}^{2}} \\
& {{\left( \sqrt{a{}_{n+1}+1} \right)}^{2}}={{\left( \sqrt{a{}_{n}+1}+1 \right)}^{2}} \\
& \sqrt{a{}_{n+1}+1}=\sqrt{a{}_{n}+1}+1 \\
& \cdots \cdots \\
\end{align}\)
