My Math Forum Proof for square root series

 Pre-Calculus Pre-Calculus Math Forum

 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:
 Originally Posted by alex77 https://ibb.co/LvJkVGZ all the terms from the LHS are equal to the two terms from the RHS. https://ibb.co/0fmVq3y
Yes but set some values of $\displaystyle x$ as a test.

 August 5th, 2019, 06:32 AM #3 Newbie   Joined: Aug 2016 From: Romania Posts: 28 Thanks: 1 @idontknow If x=10 then: https://ibb.co/6NYdD7X Is that correct? Thanks from idontknow
 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. Thanks from topsquark
August 5th, 2019, 07:28 AM   #7
Newbie

Joined: Aug 2016
From: Romania

Posts: 28
Thanks: 1

Quote:
 Originally Posted by v8archie 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.
So my so called proof is good?How are you sure that it has no mistakes?

August 5th, 2019, 08:23 AM   #8
Senior Member

Joined: Dec 2015
From: somewhere

Posts: 592
Thanks: 87

Quote:
 Originally Posted by alex77 @idontknow If x=10 then: https://ibb.co/6NYdD7X Is that correct?
Yes. The last element remains $\displaystyle s_x=-1/\sqrt{2x+1}\;$,the first element $\displaystyle s_1=1$ also remains.
So the sum is $\displaystyle s_1 + s_x =1-1/\sqrt{2x+1}$.

 Tags proof, root, series, square

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post TheAbdicatedKing Math 3 March 20th, 2018 09:16 AM jstarks4444 Number Theory 2 November 16th, 2010 12:19 PM smslca Calculus 1 June 6th, 2010 10:40 AM swm Algebra 5 March 30th, 2009 04:26 PM dekaskas Algebra 2 September 17th, 2008 07:40 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top