Search results

I'm not seeing the link between that and \sqrt{n}\leq\sum\frac{1}{\sqrt{r}}. Thanks! Why do you go from \geq to > though? Also, how did you know to use that inequality you proved initially?

Are these the rectangles you are referring to?: Also I'm lost on that last part I've quoted. How do you reach that conclusion and what does it actually mean?

Nope - I tried induction as that's what the other questions with this one were about. How would I use rectangles and trapeziums?

$Prove for $n\in \mathbb{N}$, that $\sqrt{n} \leq \sum_{r=1}^{n}\frac{1}{\sqrt{r}} \leq 2\sqrt{n}-1$. Not sure how to do this. Tried splitting the inequality up into \sqrt{n} \leq \sum_{r=1}^{n}\frac{1}{\sqrt{r}} and \sum_{r=1}^{n}\frac{1}{\sqrt{r}} \leq 2\sqrt{n}-1 and then prove these...

Re: HSC 2015 3U Marathon $Prove by mathematical induction that $\sum_{r=n}^{2n-1}2r+1=3n^2$ for $n\geq1$.

Yep. What was the answer to the third part?

I meant for the first 5 games where the player does not get a black slot. The 6th game where the player does get a black slot is 18/37.

(ii): It is 19/37 as you can either get one of the 18 red slots or the green slot - 19 slots in total. (iii): Is the answer 1 - (19/37)^5 ?

That's what I was a bit unsure about. Thanks for clearing it up, I appreciate it.

I wasn't really bothered to travel there. Figured I could do it when it comes online anyway.

It is in the first post of this thread. Here is a direct link: BOS Trials.zip

Thanks guys! I think I understand now.

Re: HSC 2015 2U Marathon \begin{align*}\textup{1. }x^2&=\sqrt{x} \\x^2-\sqrt{x}&=0 \\\sqrt{x} \left (\sqrt{x^3}-1 \right ) &=0 \\\sqrt{x}&=0\to x=0 \\\sqrt{x^3}-1&=0 \to \sqrt{x^3}=1 \to x^3 = 1\to x=1 \\\textup{Solutions are }x&=0,1. \\\end{align*} \begin{align*}\textup{3. A}&=\int^1_0...

Can someone explain how you do this? Here is an example question:

Re: HSC 2015 2U Marathon For an odd function f(-x) = -f(x). If x = 0, we have f(0) = -f(0) -> 2f(0) = 0 -> f(0) = 0. Therefore odd functions defined for x = 0 pass through the origin (0,0).

re: HSC Physics Marathon Archive The question is

%24P%28only%20Sophia%20passes%29%20%24%3D\frac{1}{2}%20\times%20\frac{3}{8}%20\times%20\frac{1}{4}%3D\frac{3}{64}%24.%20P%28only%20Gabriel%20passes%29%20%24%3D\frac{1}{2}%20\times%20\frac{5}{8}%20\times%20\frac{1}{4}%3D\frac{5}{64}%24.%20P%28only%20Elizabeth%20passes%29%20%24%3D\frac{1}{2}%20\tim...

Oh. I thought the condition would be only one passing.

Isn't it a conditional probability problem?

Depends what you consider crazy large. This year for bio and phys we have around 75, and for chem we have around 100. Is your school better at humanities than sciences?