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## #1 2006-06-04 04:28:33

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

### Luca's Puzzles (math)

1.

A geometric progression U has first term a, where

, and common ratio r, where
, the difference between the fourth and first term is equal to four times the difference between the third and second term:

a) show that

,
b) show that (r-1) is a factor of
. hence factorise.
c) hence find two possible values for the common ratio, giving youre answers in exact form
d) for the value of r for which the progression is convergenet prove that

Last edited by luca-deltodesco (2006-06-06 07:54:17)

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## #2 2006-06-04 09:45:50

Mozartmoses
Member
Registered: 2006-04-26
Posts: 10

### Re: Luca's Puzzles (math)

By the given information, we can write the equation as........

(ar^3 - a) = 4(ar^2 - ar)
=> a(r^3 - 1) = 4ar(r - 1)
=> r^3 - 4r^2 + 4r -1 = 0

I suppose, the contant term -1 is missing in the question.  Am I right?

With regards
Moses

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## #3 2006-06-05 03:06:06

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

### Re: Luca's Puzzles (math)

Mozartmoses wrote:

I suppose, the contant term -1 is missing in the question.  Am I right?

ah yeh, i thought it looked a little strange, ill change in the question

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## #4 2006-06-06 06:45:34

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

### Re: Luca's Puzzles (math)

2.
given that:

prove that:

3.
given that:

prove that

4.
Given a two vector

prove that a perpendicular two vector to a is:

Last edited by luca-deltodesco (2006-06-06 08:01:48)

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## #5 2006-07-23 03:44:01

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

### Re: Luca's Puzzles (math)

2.

,
so:

Last edited by krassi_holmz (2006-07-23 03:48:43)

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