Search found 461 matches
- Thu Jan 23, 2014 2:14 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Higher Secondary 2009/11
- Replies: 9
- Views: 7990
Re: BdMO National Higher Secondary 2009/11
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: 5193
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: 8
- Views: 12661
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: 3813
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: 5755
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: 5772
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: 6256
- Mon Feb 11, 2013 5:27 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO 2013 Higher Secondary Problem 9
- Replies: 3
- Views: 4300
- Wed Feb 06, 2013 5:19 pm
- Forum: Combinatorics
- Topic: Sum
- Replies: 7
- Views: 6694
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
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Higher Secondary 2010/10
- Replies: 2
- Views: 3660
Re: BdMO National Higher Secondary 2010/10
Please check the link for solution: viewtopic.php?f=13&t=33&p=13138#p13138