vai sol ta shundor hoise :Phlembac Adib Hasan wrote: We need two pairs of parallel lines to make a parallelogram.So the answer is $ {}^ {10} C_2 {}^8 C_2 =1260 $.
Round 3
- Nadim Ul Abrar
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$\frac{1}{0}$
Re: Round 3
ফিবোনাচ্চি ক্রমের যোগফল নির্নয় করার সাধারন সূত্র আছে কি?
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- Abdul Muntakim Rafi
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Re: Round 3
Adib Hasan: Thank you very much for a nice solution...
Nadim ul Abrar: How did u solve 7? Please explain...
Labib: Yes there are... Nadim wrote the one needed... The sum of the first n Fibonacci numbers with odd indices is what Nadim wrote...
And guys share how u proved 8 has no solution...
Nadim ul Abrar: How did u solve 7? Please explain...
Labib: Yes there are... Nadim wrote the one needed... The sum of the first n Fibonacci numbers with odd indices is what Nadim wrote...
And guys share how u proved 8 has no solution...
Man himself is the master of his fate...
Re: Round 3
অবশ্যই আছে। Wikipedia তে দেখ। খুব সোজা জিনিস।ফিবোনাচ্চি ক্রমের যোগফল নির্নয় করার সাধারন সূত্র আছে কি?
I don't think its possible to have the solution without using any calculator by your way.$f_{2012}=\frac{1}{\sqrt{5}}[(\frac{1+\sqrt{5}}{2})^{2012}-(\frac{1-\sqrt{5}}{2})^{2012}]$
I have also use almost same method. So I'm also fail to do it (without calculator.)
And without calculator it's quite boring.
হার জিত চিরদিন থাকবেই
তবুও এগিয়ে যেতে হবে.........
বাধা-বিঘ্ন না পেরিয়ে
বড় হয়েছে কে কবে.........
তবুও এগিয়ে যেতে হবে.........
বাধা-বিঘ্ন না পেরিয়ে
বড় হয়েছে কে কবে.........
- Nadim Ul Abrar
- Posts:244
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Re: Round 3
@ rafi :8. what about $p=q=r$
7, My explanation must require the figure ....
7, My explanation must require the figure ....
$\frac{1}{0}$
Re: Round 3
\[\sum^n_{k=0} f_k= f_{2n+1}-1\]Labib wrote:ফিবোনাচ্চি ক্রমের যোগফল নির্নয় করার সাধারন সূত্র আছে কি?
\[\sum^n_{k=0} f_{2k}= f_{2n+1}\]
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Nur Muhammad Shafiullah | Mahi
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Nur Muhammad Shafiullah | Mahi
Re: Round 3
Easy solution of $\boxed 8$
Let $p > q \geq r$
Then $p > \frac {q+r} 2$
But the highest divisor of $n$ may be $\frac n2$
Do the rest
Let $p > q \geq r$
Then $p > \frac {q+r} 2$
But the highest divisor of $n$ may be $\frac n2$
Do the rest
Please read Forum Guide and Rules before you post.
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
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Nur Muhammad Shafiullah | Mahi
- Nadim Ul Abrar
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Re: Round 3
*Mahi* vai isn't n is a divisor of n*Mahi* wrote: But the highest divisor of $n$ may be $\frac n2$
Do the rest
$\frac{1}{0}$
Re: Round 3
Yes, but as the case $p=q+r$ is not possible so we can strike that out.Nadim Ul Abrar wrote:*Mahi* vai isn't n is a divisor of n*Mahi* wrote: But the highest divisor of $n$ may be $\frac n2$
Do the rest
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Nur Muhammad Shafiullah | Mahi
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- Phlembac Adib Hasan
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Re: Round 3
$f_{2012} $ has 420 digits in decimal expression.[From wolframalpha]So I don't think you can find it using ordinary scientific calculators or may be by your PC!I don't think its possible to have the solution without using any calculator by your way.
I have also use almost same method. So I'm also fail to do it (without calculator.)
And without calculator it's quite boring.
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