Math Is Fun Forum

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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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

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Luca's Puzzles (math)

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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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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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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