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August 5th, 2019, 04:59 AM  #1 
Newbie Joined: Aug 2016 From: Romania Posts: 28 Thanks: 1  Proof for square root series https://ibb.co/LvJkVGZ In this image I have a sum series and I need to proove that all the terms from the LHS are equal to the two terms from the RHS. I wrote a solution but I'm not 100% certain this is correct. https://ibb.co/0fmVq3y Last edited by alex77; August 5th, 2019 at 05:01 AM. 
August 5th, 2019, 05:19 AM  #2  
Senior Member Joined: Dec 2015 From: somewhere Posts: 592 Thanks: 87  Quote:
 
August 5th, 2019, 06:32 AM  #3 
Newbie Joined: Aug 2016 From: Romania Posts: 28 Thanks: 1  
August 5th, 2019, 06:39 AM  #4 
Newbie Joined: Aug 2016 From: Romania Posts: 28 Thanks: 1 
That's how it showed in my textbook. I have no idea if what I wrote is wrong or correct. Can someone help me? 
August 5th, 2019, 07:06 AM  #5 
Newbie Joined: Aug 2016 From: Romania Posts: 28 Thanks: 1 
Anyone? There are 34 views and no hints or answers...

August 5th, 2019, 07:25 AM  #6 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra 
It looks fine to me. I would suggest writing a comment along the lines of "it's a telescopic series" to show that you really understand what's happening.

August 5th, 2019, 07:28 AM  #7 
Newbie Joined: Aug 2016 From: Romania Posts: 28 Thanks: 1  
August 5th, 2019, 08:23 AM  #8  
Senior Member Joined: Dec 2015 From: somewhere Posts: 592 Thanks: 87  Quote: So the sum is $\displaystyle s_1 + s_x =11/\sqrt{2x+1}$.  

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proof, root, series, square 
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