Under rooted

Can you help to find the value of this expression below?

$y = \sqrt{ 4 + 27 \sqrt{4 + 29 \sqrt{4 + 31 \sqrt{4 + 33\sqrt{\cdots}}}}}$

Edit: I need to prove that the above value is 29.

Thanks in advance.

#Algebra

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Comments

Value is 29. Try a few terms and evaluate it numerically. You'll see that it rapidly converges to that result.

Jack McMath - 3 years, 1 month ago

I know the answer, but how shall I prove it?, I can't find a method that shall give me the answer.

Vraj Mistry - 3 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$