C2 Geometric Progression Inequality Watch

R.J. Omega
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#1
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Hey, can anyone help me with this question?

a) 'Given the sum to infinity of the series is 5x the 1st term of the series, show r= 0.8'

b) 'Given the first term of the series is 20, find the least value of n such that the nth therm of the series is less than 1'

a) is fine, but for b) I can't figure out where to go after substituting 20=a and 0.8=r into ar^n-1<1 :confused:

Thanks in advance.
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mishmash2
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are you thinking of using logs to solve it?...hint..
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hey_its_nay
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20 * 0.8^(n-1) < 1
0.8^(n-1)<0.05
log0.8^(n-1)<log0.05
(n-1)(log0.8)<log0.05
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R.J. Omega
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So then n-1< log0.05/log0.8 would be n-1<13.4, so n=14? Thanks guys
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mishmash2
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(Original post by hey_its_nay)
20 * 0.8^(n-1) < 1
0.8^(n-1)<0.05
log0.8^(n-1)<log0.05
(n-1)(log0.8)<log0.05
You dropped a bit on their bib...
As a result you have also led them into making an error
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mishmash2
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(Original post by R.J. Omega)
So then n-1< log0.05/log0.8 would be n-1<13.4, so n=14? Thanks guys
What have you divided both sides by?
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hey_its_nay
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(Original post by mishmash2)
You dropped a bit on their bib...
As a result you have also led them into making an error
care to elaborate?
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mjtriggs
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log(0.8) is a negative. If you're dividing by it, the sign changes from < to > I believe.
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Physics Enemy
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(Original post by R.J. Omega)
So then n-1< log0.05/log0.8 would be n-1<13.4, so n=14? Thanks guys
No. And even if it was, you'd have n < 14.4, and n = 14 would be n_(max), which is the opposite of what the Q describes.

(0.8)^(n - 1) = 0.05
(n - 1)ln(0.8) < ln(0.05)

As ln(0.8) < 0:

(n - 1) > ln(0.05)/ln(0.8) = 13.43 ...
n > 14.43 ...

n_(min) = 15
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mishmash2
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(Original post by hey_its_nay)
care to elaborate?
Sure...
You have merely spoon fed a list of instructions that show no understanding of the implications of what you have suggested.

Typing out a list of instructions also doesnt assist learning, even less so when its going to lead to the wrong answer.
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hey_its_nay
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(Original post by mishmash2)
Sure...
You have merely spoon fed a list of instructions that show no understanding of the implications of what you have suggested.

Typing out a list of instructions also doesnt assist learning, even less so when its going to lead to the wrong answer.
it doesn't lead to the wrong answer
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Physics Enemy
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(Original post by hey_its_nay)
it doesn't lead to the wrong answer
Correct, don't know what he's complaining about.
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Farhan.Hanif93
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(Original post by Physics Enemy)
Correct, don't know what he's complaining about.
Think about it this way, do you need to practice these types of questions? No. So why ruin it for people who don't fully understand it by giving the answer away without explaining what you're doing and why? He has a point.
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mishmash2
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(Original post by hey_its_nay)
it doesn't lead to the wrong answer
ok, you continue doing that then :yep:
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