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#1 2005-12-31 06:38:38
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What is the sum of the following.
squr(1+(squr(1+(squr(1+(squr(1+(squr(1+(squr(1+(...
#3 2005-12-31 06:52:16
- siva.eas
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Let
squr(1+(squr(1+(squr(1+(squr(1+(squr(1+(squr(1+(...) = x
[squr(1+(squr(1+(squr(1+(squr(1+(squr(1+(squr(1+(...)]^2 = x^2
(1+(squr(1+(squr(1+(squr(1+(squr(1+(squr(1+(...) = x^2
(squr(1+(squr(1+(squr(1+(squr(1+(squr(1+(...) = x^2 - 1
As we already said, squr(1+(squr(1+(squr(1+(squr(1+(squr(1+(squr(1+(...) = x
so
x = x^2 -1
x^2 - x - 1 = 0
From the quadratic formula
x = (-(-1) + squr( 1 - 4*1*(-1)))/(2*1) or x = (-(-1) - squr( 1 - 4*1*(-1)))/(2*1)
x = (1+ squr (5))/2 or x = (1 - squr (5))/2
x = 1.618 or x = -0.618
x = -0.618 won't work since it is negative number, so the sum is 1.618.
#4 2005-12-31 07:04:36
- Flowers4Carlos
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siva: that is a very interesting approach and one that i'm not too sure if it's true, however, it looks like you found the x-intercept and not the summation.
#5 2005-12-31 07:19:07
- krassi_holmz
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Great!
Siva is right!
Well done, Siva!
IPBLE: Increasing Performance By Lowering Expectations.
#8 2005-12-31 08:04:44
- krassi_holmz
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Number of the form
is nested radical.
Herschfeld (1935) proved that a nested radical of real nonnegative terms converges iff is bounded
Last edited by krassi_holmz (2005-12-31 08:13:42)
IPBLE: Increasing Performance By Lowering Expectations.
#9 2005-12-31 08:09:12
- MathsIsFun
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I tried it in Excel, and it reaches 1.618034 after 20 terms ...
So perhaps the answer is The Golden Mean.
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
#10 2005-12-31 08:34:53
- krassi_holmz
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I forgot to put the url back:
http://mathworld.wolfram.com/GoldenRatio.html
IPBLE: Increasing Performance By Lowering Expectations.
#12 2005-12-31 20:39:27
- krassi_holmz
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He'll call back.
IPBLE: Increasing Performance By Lowering Expectations.
#13 2006-01-01 07:21:09
- mathsyperson
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Unless he's rude, in which case he'll look at the answer and not bother to thank us. It's been known to happen.
Why did the vector cross the road?
It wanted to be normal.
#14 2006-01-01 08:23:40
- krassi_holmz
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"thank us" ???
IPBLE: Increasing Performance By Lowering Expectations.
#15 2006-01-01 08:26:20
- mathsyperson
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Well, us as a forum community. You knew what I meant.
Why did the vector cross the road?
It wanted to be normal.
#16 2006-01-01 09:19:34
- krassi_holmz
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Just a joke.
IPBLE: Increasing Performance By Lowering Expectations.
