Does the ceiling change anything?

Algebra Level 3

Given ⌈ 2 + ⌈ 2 + ⌈ 2 + ⌈ 2 + . . . ⌉ ⌉ ⌉ ⌉ = ζ \large \sqrt{\left \lceil 2 + \sqrt{\left \lceil 2+ \sqrt{ \left \lceil 2 + \sqrt{\left \lceil 2+ ... \right \rceil }\right \rceil }\right \rceil}\right \rceil } = \zeta

find ⌊ 1000 ζ ⌋ \left \lfloor 1000 \zeta \right \rfloor .


The answer is 2000.

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Hobart Pao by Hobart Pao , 23, USA

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1 solution

Sahil Jain
Oct 19, 2017

Actually, both ζ = 2 \zeta\ = 2 and ζ = 5 \zeta\ = \sqrt 5 are the solutions.

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I am unable to post complete solution because I don't know LATEX.

Sahil Jain - 3 years, 7 months ago

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can you handwrite your solution and post the picture?

Hobart Pao - 3 years, 7 months ago

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