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Arithmetic series/progression problems

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Reply 20
Avatar for cambo211
cambo211
19
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 −10−10\dfrac{-10}{-10} and then divide both sides of the inequality by 1010. Multiplying by the −10−10\dfrac{-10}{-10} brings the denominator to 11 and then you proceed to solve the inequality as usual.

He could just as easily multiplied the LHS by −1−1\dfrac{-1}{-1} and then multiplied both sides by the 0.10.1 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?
(edited 10 years ago)
Reply 21
Avatar for lolface12
lolface12
OP
Original post by cambo211
What he did was multiply the LHS by −10−10\dfrac{-10}{-10} and then divide both sides of the inequality by 1010. Multiplying by the −10−10\dfrac{-10}{-10} brings the denominator to 11 and then you proceed to solve the inequality as usual.

He could just as easily multiplied the LHS by −1−1\dfrac{-1}{-1} and then multiplied both sides by the 0.10.1 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.
Reply 22
Avatar for cambo211
cambo211
19
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 :h:

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


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


(10)(1.1n−1)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 1−1.1n1-1.1^n by the −1-1 that comes with the 1010

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

Any clearer?
(edited 10 years ago)
Reply 23
Avatar for lolface12
lolface12
OP
Original post by cambo211
No problem :h

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


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


(10)(1.1n−1)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 1−1.1n1-1.1^n by the −1-1 that comes with the 1010

(1−1.1n)×−1=−1+1.1n=1.1n−1(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
Reply 24
Avatar for cambo211
cambo211
19
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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