Generally, I know how to calculate the sq roots or cube roots, but I am confused in this question, don't know how to do this:
$$\sqrt{20+\sqrt{20+\sqrt{20 + \cdots}}}$$
Note: Answer given in the key book is $5$.
Not allowed to use calculator.
Answer
HINT:
Let $\displaystyle S=\sqrt{20+\sqrt{20+\sqrt{20+\cdots}}}$ which is definitely $>0$
$\displaystyle\implies S^2=20+S\iff S^2-S-20=0$
But we need to show the convergence of the sum
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