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yeah lads

Re: First Year Uni Calculus Marathon Since this is one of the easier questions ill solve this : \lim_{n\rightarrow \infty }\left(1+\frac{x}{n}\right)^n \ <=> \lim_{n\rightarrow \infty } e^{n\ln{(1+\frac{x}{n})}} $ Applying L'hopitals rule we get $ e^x = \lim_{n\rightarrow \infty...

Yep. So the basic idea is which steps can I be on as I take my last step: a_n = a_{n-1} ($ If my last step is 1 $) + _{n-3} ($ If my last step is 3 $ ) Extra question: Write a recurrence for the amount of ways I can climb n stairs using 1,2,3... or n step(s). Should be easy now...

This is even going beyond the course of MX2... It's evil to leave them wandering... Hint: Instead of counting up count the ways you can finish.

In how many ways can you climb 15 steps by only taking 1 or 3 steps at a time?

$ i) Let P(n) be the proposition that: $ x^n - x F_n - F_{n-1} = 0 $ for some x which satisfies $ x^2 - x - 1 = 0. $ Consider P(2) : $ x^2 - x F_1 - F_ 0 = 0 = x^2 - x - 1 $ and thus P(2) is true. $ $ Let k be an integer for which P(k) is true: $ x^n - x F_k - F_{k-1} =...

$ Let P(n) be the proposition that : $ (1+2+3+\dots+n)^2 = 1^3+2^3+3^3+\dots+n^3 $ Consider $ P(1): (1)^2 = 1^3 = 1 $ Which is true. $ $ Let k be an integer for which P(k) is true: $ (1+2+3+ \dots + k)^2 = 1^3 + 2^3 + \dots + k^3 $ Consider P(k+1): $ \\ (1+2+\dots...

Re: HSC 2016 4U Marathon The return of Sy123.

Go on unsw library site and search for it there.

Re: HSC 2016 MX2 Combinatorics Marathon What if he actually had a heart attack and we all thought it was a joke ? O.o

My discrete maths teacher wrote the hsc question lel

Nah he sent me the last question, I have too much uni work to catch up on and I only have $1 in my bank account so couldnt come :P

Question 16 was a probability question + integration/ proving e was irrational sort of question.

Can I come just for the question paper? Last time I remember it was like silk.

Re: HSC 2016 3U Marathon Have a video of KoA doing these bottle flips:

Re: HSC 2016 3U Marathon Just write : "The proposition P(n) is true for all positive integers n." *Assuming you said "let the proposition/statement be P(n)."* Also as Integrand says it is not theoretically right as because when do you stop counting ? (As Prof. Peter Brown said) Mathematical...

Re: HSC 2016 3U Marathon "Riemann sums" *In a strong German accent*.

Re: HSC 2016 3U Marathon Damn just do rectangles lel... Someone do the second limit.

Re: HSC 2016 3U Marathon The induction is left uncompleted but heres a follow up : $ Prove that: $ \frac{2n}{3} \cdot \sqrt{n} \leq \sqrt{1} + \sqrt{2} + ... + \sqrt{n} \leq \frac{(4n+3)}{6} \cdot \sqrt{n}

Re: HSC 2016 3U Marathon New Question: $ Prove by induction : $ \sqrt{1} + \sqrt{2} + ... + \sqrt{n} \geq \frac{2n}{3} \cdot \sqrt{n} * Also think of an alternate way of proving this *