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Algebra Level 2

1 + 2008 1 + 2009 1 + 2010 1 + 2011 × 2013 = ? \sqrt{1 + 2008\sqrt{1 + 2009\sqrt{1 + 2010 \sqrt{1 + 2011 \times2013}}}} = \ ?

2009 1999 2008 2010

Akshat Sharda by Akshat Sharda , 21, India

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3 solutions

John Gilling
Jun 18, 2015

Note that 1 + ( x − 1 ) ( x + 1 ) = x 2 1+(x-1)(x+1) = x^2 , and so the innermost square root evaluates to 2012, the next outermost to 2011, the next to 2010, and the full expression to 2009.

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Sakshi Rathore
Jul 12, 2015

apply Ramanujan formula>>>>i guess Harshi Singh will tell us..

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Rajath Sharma
Jul 2, 2015

2011*2013 can be written as (2012+1)(2012-1).Therefore the inner most square root reduces to 2012^2.By continuing the same process throughout, we get the solution as 2009.

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