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August 5th, 2019, 04:59 AM   #1
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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.
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August 5th, 2019, 05:19 AM   #2
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Quote:
Originally Posted by alex77 View Post
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.
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August 5th, 2019, 06:32 AM   #3
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@idontknow If x=10 then:
https://ibb.co/6NYdD7X
Is that correct?
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August 5th, 2019, 06:39 AM   #4
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That's how it showed in my textbook. I have no idea if what I wrote is wrong or correct.
Can someone help me?
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August 5th, 2019, 07:06 AM   #5
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Anyone? There are 34 views and no hints or answers...
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August 5th, 2019, 07:25 AM   #6
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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.
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August 5th, 2019, 07:28 AM   #7
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Originally Posted by v8archie View Post
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?
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August 5th, 2019, 08:23 AM   #8
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Quote:
Originally Posted by alex77 View Post
@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 $\displaystyle s_1 + s_x =1-1/\sqrt{2x+1}$.
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