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Nah it's limited so you can have 1.

Anyone seen attack on titan s4 ep7 freaking epic

5 (b) For an infinite GP |r|<1 so |\phi x|<1 \implies |x|<\frac{1}{\phi} since |\phi|=\phi. Therefore x\neq \frac{1}{\phi} Also \phi>1 \implies \frac{1}{\phi}<1 so x\neq 1. Another more intuitive explanation, x=\frac{1}{\phi} satisfies the quadratic in the denominator for s(x) so we are dividing...

Lol the paper is already impossible to do timed (even for a freaking olympiad medalist), and it's getting even harder geez.

Ok Ill show my thought process anyways. Question 5, the first thing I see is the result as well as the condition: |x|<\frac{1}{\phi}. Without even thinking about how to solve it, the condition should look really familiar if you have done sequences/series, it's very similar to the condition for...

Nah its not, it's just series.

Ill show you my full thought process for q5 tommorow if you want from seeing the question to answering.

Trust me every question I've answered on this site is nothing compared to BOS.

We will see haha

they really shouldnt have removed harder 3U.

Since I have no life Ill attempt these (some working may be left out due to sheer number of questions): 1. (a) n=1 is easy to see. Assume: F_1 + F_2 + F_3 + ... + F_k = F_{k+2} - 1. Add F_{k+1} to both sides: F_1 + F_2 + F_3 + ... + F_k +F_{k+1}= F_{k+2}+F_{k+1} - 1, now use the definition of...

bad

Directrix do you feel remorse now?

1,1,7,8,15 for 2u,3u,chem,phys,2u eng in year 11 top 50 school ( I wont say which school ofc). Theres about a 150 people doing each course.

The concept lol. You defending a random guy on the internet only to be backstabbed by the same guy.

Im not that up to date with the BOS lore. I've also heard HSCbuzman being tossed around, where does he fit in?

Is velocifire and directrix the same acc?

You could have done \sin(\theta)=\cos\left(\frac{\pi}{2}-\theta\right) where \theta=\sin^{-1}(x) which is a basic definition that is allowed, to prove the inverse formula. Also like Trebla said you could do \cos(2\cos^{-1}(x))=3x+1 \implies 2x^2-1=3x+1 I think this is a more logical progression.

I think if you explained why \sin^{-1}(x)+\cos^{-1}(x)=\frac{\pi}{2} and added some explanation between steps your proof would have made more sense.

If it took you three lines to explain that it isn't so obvious?