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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!)...
by sourav das
Thu Jan 23, 2014 2:14 pm
 
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Higher Secondary 2009/11
Replies: 9
Views: 1991

Re: BdMO National 2013: Secondary 5

I got different solution : $\frac{3125 \sqrt{3}}{4}$ square unit... Ratio $\frac{5}{12}$
by sourav das
Mon Jan 13, 2014 1:48 pm
 
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2013: Secondary 5
Replies: 4
Views: 827

Re: BdMO National 2013: Secondary 8, Higher Secondary 6

@Fatin, Not Clear to me at all! Faulty Solution. First, try to explain it clearly.
by sourav das
Mon Jan 13, 2014 1:31 pm
 
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2013: Secondary 8, Higher Secondary 6
Replies: 7
Views: 1527

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...
by sourav das
Mon Jul 01, 2013 11:40 am
 
Forum: Algebra
Topic: F.E. (2012 Croatian TST)
Replies: 2
Views: 881

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...
by sourav das
Tue Feb 19, 2013 10:44 pm
 
Forum: Social Lounge
Topic: Math Olympiad type coaching
Replies: 4
Views: 1603

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:...
by sourav das
Fri Feb 15, 2013 7:27 am
 
Forum: Social Lounge
Topic: Happy VALENTINE
Replies: 4
Views: 1582

Re: BdMO 2013 Higher Secondary Problem 8

viewtopic.php?f=25&t=916

This will help a lot. But my solution involves harmonic conjugate.
by sourav das
Mon Feb 11, 2013 5:29 pm
 
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2013: Higher Secondary 8
Replies: 6
Views: 1104

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...
by sourav das
Wed Feb 06, 2013 5:19 pm
 
Forum: Combinatorics
Topic: Sum
Replies: 7
Views: 1543
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