2016 HSC Past Paper Question (1 Viewer)

[Andy005]

Q(IV) I don't exactly understand the solution to this question.

Thanks.

 

[fan96]

Given that

for some .

Set to get



That red expression on the RHS looks very similar to the LHS.

Set to get



Substitute (2) back into (1) to get:



Set to get



Substitute (4) back into (3) to get:



If you look at (1), (3) and (5):





It's pretty clear what is happening on the RHS.

If you keep repeating this process, then for any finite you will eventually get



So how many minus signs are on the RHS? Well let's look at those equations again:





That red number happens to be the same as the number of minus signs on the RHS.

Now so when we eventually reduce that term on the RHS to then there will be minus signs on the RHS.

That is,



Note that the LHS contains and is not defined. Therefore we need .