Q1231 Given $a>0$, prove that
$$ \underbrace{\sqrt{a+\sqrt{a+\cdots+\sqrt{a}}}}_{n \text{ times}} <\frac{1+\sqrt{4a+1}}{2}.$$
Q1231 Given $a>0$, prove that
$$ \underbrace{\sqrt{a+\sqrt{a+\cdots+\sqrt{a}}}}_{n \text{ times}} <\frac{1+\sqrt{4a+1}}{2}.$$