Radical Time.. :D ----> 2

Algebra Level 3

Evaluate.

2012+√1 1-√2012 1+√2013 1+√2012

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2 solutions

Himanshu Mittal
Oct 29, 2014

There is error in question. Second term onward the denominator term should have positive sign. Then only cancellation will happen

I dont think so

1 i + 1 i = i + 1 + i \frac{1}{\sqrt{i+1}-\sqrt{i}} = \sqrt{i+1}+\sqrt{i}

So the problem now seems to be : 2012 + 2011 i = 1 2010 i + 1 + i \sqrt{2012}+\sqrt{2011} - \sum_{i=1}^{2010} \sqrt{i+1}+\sqrt{i}

Mohamed Laghlal - 6 years, 4 months ago

ahahah. :3

Christian Daang - 6 years, 7 months ago

No need... If we rationalize, it will undergo to:

√2012 + √2011 - √2011 + √2010 - √2009 + √2008 + ... + √1 = 1 + √2012

Christian Daang - 6 years, 7 months ago
Christian Daang
Oct 28, 2014

let a = 2012

then, rationalize the denominator, and all are being cancel except √1 and √2012

Therefore, the answer is 1+√2012 .

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