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-1+2^1/2-3^1/2+4^1/2-5^1/2............+2014^1/2

 Jan 11, 2016

Best Answer 

 #5
avatar+2498 
+5

i mean it s a "brain easer" problem there is need to be easy way

 Jan 11, 2016
 #1
avatar+2498 
0
 Jan 11, 2016
edited by Solveit  Jan 11, 2016
 #2
avatar+2498 
+5

-1+2^1/2-3^1/2+4^1/2-5^1/2............+2014^1/2  up to ^2

 

it will be -1+2-3+4-5......-2013+2014=x^2

 

x^2=1

x=1

 Jan 11, 2016
 #3
avatar+33616 
+5

-1+2^1/2-3^1/2+4^1/2-5^1/2............+2014^1/2 ≈ 22.061

 

You can't square each individual term Solveit.  If x = -1+2^1/2-3^1/2+4^1/2-5^1/2............+2014^1/2

it is not true that x^2 = -1 + 2 -3 + 4 -5 +...-2013 + 2014

 Jan 11, 2016
edited by Alan  Jan 11, 2016
edited by Alan  Jan 11, 2016
 #4
avatar+2498 
+5

how did you calculated this ?

 Jan 11, 2016
 #5
avatar+2498 
+5
Best Answer

i mean it s a "brain easer" problem there is need to be easy way

Solveit Jan 11, 2016
 #6
avatar+33616 
+5

I just used a piece of numerical software.  I also thought it was a brain teaser at first and looked for a simpler way; however, I couldn't see one! 

 

Now if the individual terms were squared instead of square-rooted, it would be a different matter.

 Jan 11, 2016
edited by Alan  Jan 11, 2016

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