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what is the value of x?

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- April 1st 2012, 03:10 AMMhmh96The value of x
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what is the value of x? - April 1st 2012, 03:17 AMProve ItRe: The value of x
Wolfram didn't give an exact answer, so I doubt there is one...

sum 1/(Sqrt[2n] + Sqrt[2*(n+1)] ) with n from 0 to 1003 - Wolfram|Alpha - April 1st 2012, 03:24 AMprincepsRe: The value of x
- April 1st 2012, 03:37 AMMhmh96Re: The value of x
Helpful answers,thanks !

- April 1st 2012, 07:01 AMWilmerRe: The value of x
FOR k = 0 to 2006 STEP 2

x = x + 1 / [SQRT(k) + SQRT(k+2)]

NEXT k

x = 22.4053565...

SURPRISE(?): x^2 = 502 (integer) (Wondering) - April 1st 2012, 08:22 PMbrowni3141Re: The value of x
It appears that from n = 0 to k is

It is almost certain that - April 2nd 2012, 08:16 AMWilmerRe: The value of x
Well, for all the good this'll do:

1 / [SQRT(n) + SQRT(n + 2)] = SQRT{[n + 1 - SQRT(n^2 + 2n)] / 2} - April 9th 2012, 06:43 PMbrowni3141Re: The value of x
I'm surprised no one was able to figure this out until now (including me). It's actually fairly simple.

Now it is a telescoping series.