Question

★ STANDARD QUESTION 4 ★

★ CONTENT QUALITY SUPPORT REQUIRED ★

Evaluate -
$\sqrt{1 + 2 \sqrt{1 + 3 \sqrt{1 + 4 \sqrt{1 + 5... \infty } } } }$
★ LEVEL - 100 ★

Answer 1

Hey friend, Harish here.

Here is your answer:

The answer is 3 .

i)

$3 = \sqrt{9}$

$= \sqrt{1+2.4}$

$= \sqrt{1+2 \sqrt{16} }$

$= \sqrt{1+2 \sqrt{1+3.5} }$

$= \sqrt{1+2 \sqrt{1+3 \sqrt{25} } }$

$= \sqrt{1+ 2\sqrt{1+3 \sqrt{1+4.6} } }$

$= \sqrt{1+2 \sqrt{1+3 \sqrt{1+4 \sqrt{36} } } }$

$= \sqrt{1+2 \sqrt{1+3 \sqrt{1+4 \sqrt{1+5... \infty} } } }$

Therefore it is equal to 3.
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Answer 2

Step-by-step explanation:

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