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# Assume the expression Sqrt(2 + Sqrt(2 + Sqrt(2 + Sqrt(2 +

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Joined: 07 Jul 2003
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Assume the expression Sqrt(2 + Sqrt(2 + Sqrt(2 + Sqrt(2 + [#permalink]

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29 Jul 2003, 20:08
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Assume the expression Sqrt(2 + Sqrt(2 + Sqrt(2 + Sqrt(2 + ...))))) ultimatimately converges to X. What is X?

(A) Sqrt(3)
(B) 1 + Sqrt(2)
(C) 1 + Sqrt(3)
(D) 2
(E) Sqrt(3)*Sqrt (2)
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

Manager
Joined: 25 Jun 2003
Posts: 93

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29 Jul 2003, 20:45
Let X = Sqrt(2 + Sqrt(2 + Sqrt(2 + Sqrt(2 + ...)))))

==> X = SQRT(2+X)

or X^2 = 2 + X

Solving for X ,we get 2 and -1

So I choose D
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Brainless

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Joined: 15 Aug 2003
Posts: 3454

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30 Sep 2003, 17:05
Brainless wrote:
Let X = Sqrt(2 + Sqrt(2 + Sqrt(2 + Sqrt(2 + ...)))))

==> X = SQRT(2+X)

or X^2 = 2 + X

Solving for X ,we get 2 and -1

So I choose D

Brain

Can you explain this please
Manager
Joined: 25 Jun 2003
Posts: 93

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30 Sep 2003, 18:55
praetorian123 wrote:
Brainless wrote:
Let X = Sqrt(2 + Sqrt(2 + Sqrt(2 + Sqrt(2 + ...)))))

==> X = SQRT(2+X)

or X^2 = 2 + X

Solving for X ,we get 2 and -1

So I choose D

Brain

Can you explain this please

Praet,

Sqrt(2 + Sqrt( 2 + sqrt(2 + sqrt(2 + ............)))) --- (1)

Say x = Sqrt( 2 + sqrt(2+ ..............)))

means (1) will be equivalent to x = Sqrt(2 + x)
( bold part equated to x )

or X^2 = 2 + X

Let me know if this is OK
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Brainless

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Joined: 15 Aug 2003
Posts: 3454

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30 Sep 2003, 21:03
Brainless wrote:
praetorian123 wrote:
Brainless wrote:
Let X = Sqrt(2 + Sqrt(2 + Sqrt(2 + Sqrt(2 + ...)))))

==> X = SQRT(2+X)

or X^2 = 2 + X

Solving for X ,we get 2 and -1

So I choose D

Brain

Can you explain this please

Praet,

Sqrt(2 + Sqrt( 2 + sqrt(2 + sqrt(2 + ............)))) --- (1)

Say x = Sqrt( 2 + sqrt(2+ ..............)))

means (1) will be equivalent to x = Sqrt(2 + x)
( bold part equated to x )

or X^2 = 2 + X

Let me know if this is OK

x = Sqrt(2 + x)

how are the two x's same...are we approximating that the "x on the left"[/b] is equal to "x on the right"
Intern
Joined: 29 Aug 2003
Posts: 47
Location: Detroit, MI

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01 Oct 2003, 07:32
how are the two x's same...are we approximating that the "x on the left"[/b] is equal to "x on the right"[/quote]

Yes, it's an approximation. We can do this for infinite sequences such as this.
01 Oct 2003, 07:32
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# Assume the expression Sqrt(2 + Sqrt(2 + Sqrt(2 + Sqrt(2 +

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