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Re: HSC 2013 4U Marathon Is the answer 1-1/n!-n/(n+1)! ?

Re: HSC 2013 3U Marathon Thread What I did here was use sum of the following geometric series: (1+x)^m-1 +(1+x)^m+.........+(1+x)^m+n-1 =[ (1+x)^m+n -(1+x)^m-1/x] Then I equated coefficients of x^m-1 and rewrote them in the form (m+n)!/m!n!....Does it work??

Re: HSC 2013 3U Marathon Thread I showed the result but having the m/1! was necessary---> Are you sure there isn't a mistake? I may be wrong though.

Re: HSC 2013 3U Marathon Thread I'm not getting the +g either for some reason. How did you solve it?

re: HSC Physics Marathon Archive I think we use exact values throughout working(stored in our calculators), then round our final answer...but I was just rushing through the question so wasn't paying much attention to decimal places and stuff.

Re: HSC 2013 3U Marathon Thread I think i'm missing something here, but how do we get this? When we integrated didn't the LHS become [(1+x)^n+1/n+1] +c ?

re: HSC Physics Marathon Archive I'm not too sure about my answer. Let y=0 be ground level y=1/2 a(y)t^2 + u(y) +100 Uy=0, as it is released horizontally---> So y=1/2 a(y)t^2 + 100 (1) x= U(x)t, Ux=10---> x=10t (2) tan45=y/x, so y=x Equating (1) and (2), we get a quadratic equation...

Re: HSC 2013 3U Marathon Thread I'm thinking of expanding (1+x)^n, integrating, sub x=0 to find c, then let x=1 call this (1) Repeat the process but in the final step sub x=-1 call this (2) Then (1)-(2) will yield you a similar result---> But with 2^n on the numerator on the LHS???

Re: HSC 2013 4U Marathon Dividing doesn't preserve the inequality, but can we get away with using logs then subtracting? Like ln(1-x)>=M ln(1+x)>=N Then saying ln(1-x/1+x) >= M-N Either way I wouldn't know how to use the fact that x(1)+x(2)+....+x(n)= 1/2 in this method.

Re: HSC 2013 4U Marathon Binomial expansion of (1-x^2)^n, integrate both sides between limits of x=1 and x=0. Weird thing is i'm getting an extra 2n+1 on the denominator on the RHS of the expression, maybe I integrated incorrectly. Isn't integral of (1-x^2)^n from 0 to 1...

Re: HSC 2013 4U Marathon Ok, that makes sense, so proving that f(n) is increasing for n>1 should suffice? I'm thinking of differentiating using logarithms---> but maybe this method is going a bit overboard.

Re: HSC 2013 4U Marathon Not too confident with my solution here. But i'm getting something along the lines of Let a(1)=1-x(1)....continue this for 1,2,3...n So on the LHS we get (n-1/2)/n >= nth root of what we want on the LHS numerator in our final expression. ....(1) Similarly, Let...

Re: HSC 2013 4U Marathon tanx= m(1) -m(2)/1+m(1)m(2) Where x= (n-2)*180/n Rearranging m(1)m(2) = (m(1)-m(2) /tanx )-1 ....(1) Rewrite (1) for all combinations m(2)m(3).....m(n)m(1) Then add side by side. I think?

Re: HSC 2013 3U Marathon Thread Hmm...this question looks familiar. Is it something like using the binomial expansion for (1+x)^n, then multiplying both sides by x, integrating both sides (the LHS should have an expression that's slightly harder to integrate than usual), sub in x=0 to find the...

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Its alright :) Are you planning to do the first hand prac paper??