C2 math - Little help here?.. Watch

Sokka
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#1
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I'm stuck on this geometric progressions question - it's the last one in the book and I've struggled to get here without any help and then i'm baffled by this part, soo, little help plzz?



I did most of part a) here:


They say you have to make the difference between the sum of n terms and the sum to infinity equal to quarter of the nth term. Quarter of the nth term is: 10x0.2^n as shown in my working out. I'm trying to get the last equation shown in my working out EQUAL to 10x0.2^n but I don't know how to manipulate it to get the required result. Basically, how do you get: 10 - 8 x (1-0.2^n / 1-0.2) -----> 10x0.2^n

tyvm if anyone manages to help me!!
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Sokka
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Sokka
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Zishi
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IS what you posted in second diagram the correct answer? If yes, then I'll try to solve it and explain your mistake.
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Sokka
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(Original post by Zishi)
IS what you posted in second diagram the correct answer? If yes, then I'll try to solve it and explain your mistake.
its not the answer, it's part of my working out.
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Zishi
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(Original post by Sokka)
its not the answer, it's part of my working out.
Seeing first part of your image makes me think that why'd you multiply 8 x 0.5n-1 by 1/4? That's mistake.
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Sokka
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(Original post by Zishi)
Seeing first part of your image makes me think that why'd you multiply 8 x 0.5n-1 by 1/4? That's mistake.
because it says that the sum to infinity and the sum of n terms is the same as quarter of the nth term, therefore, it is wise to work out quarter of the nth term first so you can compare it to the difference...
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