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#1 2010-10-30 08:45:41
- alice 9
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- Registered: 2010-10-06
- Posts: 6
cauchy
Let a<b let X1=a and X2=b and
Xn+2 = Xn+1 /2 +Xn/2 in another way Xn+2 = Xn+1 +Xn all over 2
Follow these steps to show that Xn Cauchy
1) Draw picture and let L=b-a
2) Use induction to show that absolute value l xn+1 xnl = L/2^(n-1)
3) Conclude that sequence Xn is Cauchy
Find a Cauchy sequence in (0,1) that does not converge to a point of (0.1)
Last edited by alice 9 (2010-10-30 16:42:32)
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#2 2010-12-13 12:03:54
- JaneFairfax
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- Registered: 2007-02-23
- Posts: 6,868
Re: cauchy
Hint:
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