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junior college 2 | H2 Maths
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how to solve this q
Date Posted: 4 years ago
Views: 498
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done
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clear
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The proving part
Date Posted:
4 years ago
thank u so much!!
thanks!!
done
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clear
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The calculation part. I assume you are aware of how to compute the sum of a geometric series.
Date Posted:
4 years ago
how do u get the 3rd step for the 3rd section though? :’)
2r is the same as saying
2r - 1 + 1, or
(2r - 1) + 1
We need to introduce the -1 and +1 on our own, because we need to use the results from part i which involve (2r - 1). The +1 which we introduce after introducing -1 is just to maintain equality (ie “return” what is “borrowed”).
2r - 1 + 1, or
(2r - 1) + 1
We need to introduce the -1 and +1 on our own, because we need to use the results from part i which involve (2r - 1). The +1 which we introduce after introducing -1 is just to maintain equality (ie “return” what is “borrowed”).
You can include this third step after the second step by simply writing 2r as 2r - 1 + 1 as an intermediary before you proceed to my written third step.
In other words,
summation (r * 2^-r)
= 1/2 * summation (2r * 2^-r)
= 1/2 * summation [(2r - 1 + 1) * 2^-r]
= we just multiply like a (b + c) = ab + ac
= 1/2 * summation [(2r - 1) * 2^-r] + 1/2 * summation [1 * 2^-r]
= ...
In other words,
summation (r * 2^-r)
= 1/2 * summation (2r * 2^-r)
= 1/2 * summation [(2r - 1 + 1) * 2^-r]
= we just multiply like a (b + c) = ab + ac
= 1/2 * summation [(2r - 1) * 2^-r] + 1/2 * summation [1 * 2^-r]
= ...
thank you so much for your clear explanation! i understand it now! :))
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