Arithmetic series/progression problems Watch

cambo211
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#21
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#21
(Original post by lolface12)
Is multiplying the LHS here done to get rid of the fraction? I know that near the end i would Ln to work out what n is and get the answer from there, i know too simplify 1000 before that too. But it's just the getting there part which i am struggling to grasp. Thanks for your help so far.

In the example i am struggling to work out how he got rid of the fraction by multiplying it by -10/-10 in the LHS. It's probably really simple but i just can't see it and what to do from that point
What he did was multiply the LHS by \dfrac{-10}{-10} and then divide both sides of the inequality by 10. Multiplying by the \dfrac{-10}{-10} brings the denominator to 1 and then you proceed to solve the inequality as usual.

He could just as easily multiplied the LHS by \dfrac{-1}{-1} and then multiplied both sides by the 0.1 which gives the same result without introducing new numbers to worry with. Either way the results are the same and you should use whichever way makes more sense to you.

Can you see where to go with question 2 now?
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lolface12
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#22
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#22
(Original post by cambo211)
What he did was multiply the LHS by \dfrac{-10}{-10} and then divide both sides of the inequality by 10. Multiplying by the \dfrac{-10}{-10} brings the denominator to 1 and then you proceed to solve the inequality as usual.

He could just as easily multiplied the LHS by \dfrac{-1}{-1} and then multiplied both sides by the 0.1 which gives the same result without introducing new numbers to worry with. Either way the results are the same and you should use whichever way makes more sense to you.

Can you see where to go with question 2 now?
Sorry but i can't. The n is confusing me when multiplying the top of the LHS fraction. I am still finding it confusing. How did multiplying the LHS by -10/-10 give him that answer in the 3rd line. i just don't understand that. Maybe i'm a little slow but it's hurting my brain working out how that answer is there. 1-1.1n suddenly goes to 1.1n - 1. Just confused. Can you show me the working out to reach the next line for this question? It would help me undestand it finally.
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cambo211
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#23
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#23
(Original post by lolface12)
Sorry but i can't. The n is confusing me when multiplying the top of the LHS fraction. I am still finding it confusing. How did multiplying the LHS by -10/-10 give him that answer in the 3rd line. i just don't understand that. Maybe i'm a little slow but it's hurting my brain working out how that answer is there. 1-1.1n suddenly goes to 1.1n - 1. Just confused. Can you show me the working out to reach the next line for this question? It would help me undestand it finally.
No problem

\dfrac{1-1.1^n}{-0.1}\times\dfrac{-10}{-10}


\dfrac{(-10)(1-1.1^n)}{(-10)(-0.1)}


\dfrac{(10)(1.1^n-1)}{1} The numerator here is the bit that i think you're struggling getting to.


All he's done is multiply the 1-1.1^n by the -1 that comes with the 10

(1-1.1^n)\times-1=-1+1.1^n=1.1^n-1

Any clearer?
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lolface12
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#24
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#24
(Original post by cambo211)
No problem :h

\dfrac{1-1.1^n}{-0.1}\times\dfrac{-10}{-10}


\dfrac{(-10)(1-1.1^n)}{(-10)(-0.1)}


\dfrac{(10)(1.1^n-1)}{1} The numerator here is the bit that i think you're struggling getting to.


All he's done is multiply the 1-1.1^n by the -1 that comes with the 10

(1-1.1^n)\times-1=-1+1.1^n=1.1^n-1

Any clearer?

Yes mate, it is now. Thanks very very much. I'll use that method to do the same for the question i posted. Should know where to go from that point. Thanks for your help again, much appreciated
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cambo211
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#25
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#25
(Original post by lolface12)
Yes mate, it is now. Thanks very very much. I'll use that method to do the same for the question i posted. Should know where to go from that point. Thanks for your help again, much appreciated
No problem.

Let me know if you hit a bump again.
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