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HSC 2015 MX2 Marathon (archive) (1 Viewer)

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porcupinetree

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Re: HSC 2015 4U Marathon

I converted the sum into integral format:



Then I used limiting sum to get:

And then how do you evaluate that integral? t method seems a little tedious, is there a simpler way?
 

leehuan

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Re: HSC 2015 4U Marathon

Multiply by 4/4 and also multiply by sec^2x/sec^2x
Bottom can all be converted into tangents. Then just reverse chain rule.
 

Ekman

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Re: HSC 2015 4U Marathon

For part ii:







Edit: Nevermind, I only proved that they are not divisible, I didn't prove that they didn't have a common factor.
 
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Sy123

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Re: HSC 2015 4U Marathon

For part ii:







Edit: Nevermind, I only proved that they are not divisible, I didn't prove that they didn't have a common factor.
Try proving via contradiction
 

Ekman

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Re: HSC 2015 4U Marathon

You're pretty close though.
Try proving via contradiction
I'm assuming you would use a similar method but instead of using the numbers F_n, you would use the factors of those integers, and prove that the factors cannot be integers, hence proving they do not share common factors.
 
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