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

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Assume the expression Sqrt(2 + Sqrt(2 + Sqrt(2 + Sqrt(2 + [#permalink] New post 29 Jul 2003, 20:08
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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 [#permalink] New post 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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 [#permalink] New post 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
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 [#permalink] New post 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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 [#permalink] New post 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"
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 [#permalink] New post 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.
  [#permalink] 01 Oct 2003, 07:32
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