C2 math - Little help here?..Watch

#1
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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#2
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7 years ago
#3
(Original post by Sokka)
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!!
You're very close. You can write the denominator of the fraction as 0.8, or , and so using the fact that we get that your expression is equal to . You can then simplify and you should get the right answer.

(Original post by Sokka)
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#4
i would have never thought of that, thanks
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#5
buump i still don't get how to simplify that part
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7 years ago
#6

Simplifies to

And

So it becomes

Multiply out the brackets to make

Then that simplifies to:

Which is what you needed, I think.
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