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I dont think so
i + 1 − i 1 = i + 1 + i
So the problem now seems to be : 2 0 1 2 + 2 0 1 1 − ∑ i = 1 2 0 1 0 i + 1 + i
ahahah. :3
No need... If we rationalize, it will undergo to:
√2012 + √2011 - √2011 + √2010 - √2009 + √2008 + ... + √1 = 1 + √2012
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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There is error in question. Second term onward the denominator term should have positive sign. Then only cancellation will happen