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haha, fair enough. I think if you try that, it's not that bad. :) But it's still ugly.

To be honest that was how I solved it initially but when I tried to solve it without using that inequality, at extension2 level, I also had to go through a not pleasant algebraic manipulation. Just to confirm for n=2 did you multiply the inequality by $$a_{1},a_{2} , b_{1},b_{2} $$

Well, I think that question was relatively easy for this forum so I decided to share a slightly more challenging induction question: prove for every positive integer n, if $$a_{i} > 0 , b_{i}>0 $$ for all i = 1,..,n then \sum_{i=1}^{n}\frac{a_{i}b_{i}}{a_{i}+ b_{i}} \leq \frac{AB}{A+B}...

Exactly, That is the idea. :) basically you prove it for n=1 and n=2 which is obvious, then we can show if the statement is true for n=k then its true for n=k+2, that's basically what you've done with splitting it into two cases, odd and even.

HI all, This is an interesting induction question. Question: prove for every positive integer n there exist positive integers x, y ,z such that $x^{2} + y^{2} = z^{n}$

Re: HSC 4U Integration Marathon 2017 you can rearrange and to simplify the inside the integrals to get use substitution then let constant From the you can see the integrals is tan inverse of \sqrt{u^2-1} We can back track to find it in terms of theta

Hi DragonShox, This is a tough decision! I also had to face that choice when I was in high school. I was getting around 50-60 in chemistry but I was more interested in music and It was more intuitive to me compare to chemistry. When I dropped chemistry, I felt really relaxed and I got more...