√2 ≈ 1.4.
√3 ≈ 1.7.
Thus:
√(2 + √(2 + √2)) ≈ √(2 + √3.4) ≈ √(2 + 1.8) ≈ √3.8 ≈ a little less than 2.
The subsequent values in the sequence -- all of them VERY SMALL -- will bring the sum closer and closer to 2.
The correct answer is B.
A less GMAT-friendly approach:
Let x = √(2 + √(2 + ...))
Since the sequence is infinite:
x = √(2 + √(2 + √(2 + ...)))
Using the first statement, we can replace the red portion in the second statement with x:
x = √(2 + x)
Squaring both sides:
x² = 2 + x
x² - x - 2 = 0
(x-2)(x+1) = 0.
x = 2 or x = -1.
Since the sum must be positive, x=2.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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