## Search found 461 matches

Thu Jan 23, 2014 2:14 pm
Topic: BdMO National Higher Secondary 2009/11
Replies: 9
Views: 4907

Looks like I still have some gun powder left in my gun :D . Sketch Solution: Given Statement $=\sum^{\infty}_{m\neq n,m=1,n=1}\left ( \frac{m^2n}{3^m(m3^n+n3^m)}+ \frac{n^2m}{3^n(n3^m+m3^n)} \right )+ \sum^{\infty }_{m=1}\frac{m^3}{2.3^{2m}.m}$ (A tricky arrangement!) $=\frac{1}{2}\left ( \sum^{\inf... Mon Jan 13, 2014 1:48 pm Forum: National Math Olympiad (BdMO) Topic: BdMO National 2013: Secondary 5 Replies: 4 Views: 2896 ### Re: BdMO National 2013: Secondary 5 I got different solution :$\frac{3125 \sqrt{3}}{4}$square unit... Ratio$\frac{5}{12}$Mon Jan 13, 2014 1:31 pm Forum: National Math Olympiad (BdMO) Topic: BdMO National 2013: Secondary 8, Higher Secondary 6 Replies: 7 Views: 4180 ### Re: BdMO National 2013: Secondary 8, Higher Secondary 6 @Fatin, Not Clear to me at all! Faulty Solution. First, try to explain it clearly. Mon Jul 01, 2013 11:40 am Forum: Algebra Topic: F.E. (2012 Croatian TST) Replies: 2 Views: 2226 ### F.E. (2012 Croatian TST) Find all$f:R\rightarrow R$satisfying$ f(x^2+f(y))=(f(x)+y^2)^2$My Solution Sketch i)$f(x)=f(-x)$ii)$f(x)\geq 0$iii)$f(x)=f(y)$implies$x=\pm y$iv)$P(x,\sqrt(f(y)))$and swap$(x,y)$v)$f(x^2+y^2)=(f(x)+f(y))^2$vi)$f(0)=0$or$f(0)=.5$(Doesn't satisfy the equation) vii)$f(x^2)=(f(x))^2$v... Tue Feb 19, 2013 10:44 pm Forum: Social Lounge Topic: Math Olympiad type coaching Replies: 4 Views: 3480 ### Re: Math Olympiad type coaching Is there any Math Olympiad coaching or something like this in Dhaka? দুনিয়ায় সব কিছু বাংলাদেশের পড়ালেখার মত না; বরঞ্চ অন্য কোন দেশে "পড়ালেখায় ভালো করা" এর জন্য কোচিং, স্যারদের কাছে পড়া, গাইড পড়া এত প্রচলিত বলে মনে হয় না। আমার মতে বাংলাদেশে পড়ালেখা কে পণ্য করে তুলতে আমাদের ভূমিকাও কম নয়। য... Fri Feb 15, 2013 7:27 am Forum: Social Lounge Topic: Happy VALENTINE Replies: 4 Views: 3587 ### Re: Happy VALENTINE :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: জীবনের এতগুলো বসন্ত কেটে গেল; তবু আমি..... :cry: :cry: :cry: :cry:... Mon Feb 11, 2013 5:29 pm Forum: National Math Olympiad (BdMO) Topic: BdMO National 2013: Higher Secondary 8 Replies: 6 Views: 3479 ### Re: BdMO 2013 Higher Secondary Problem 8 viewtopic.php?f=25&t=916 This will help a lot. But my solution involves harmonic conjugate. Mon Feb 11, 2013 5:27 pm Forum: National Math Olympiad (BdMO) Topic: BdMO 2013 Higher Secondary Problem 9 Replies: 3 Views: 2660 ### Re: BdMO 2013 Higher Secondary Problem 9 Wed Feb 06, 2013 5:19 pm Forum: Combinatorics Topic: Sum Replies: 7 Views: 4063 ### Re: Sum Note that:$(a+\omega )^n+(a+\omega ^2)^n+(a+1)^n=3\sum_{i=0}^{\infty}\binom{n}{3i}a^{n-3i}$Where$1+\omega+\omega^2=0$and$\omega^3=1$Now,$\sum_{i=0,j=0}^{\infty}\binom{n}{3i}\binom{n-3i}{3j}=\sum_{i=0}^{\infty}\binom{n}{3i}\left [ \sum_{j=0}^{\infty}\binom{n-3i}{3j}\right ]=\sum_{i=0}^{\inf...
Tue Jan 29, 2013 4:55 pm