২০১৩ এর প্রস্তুতি পর্ব (১)
0,1,2,10,11,12,20....এই ধারার 50 তম পদটি কত ?
Re: ২০১৩ এর প্রস্তুতি পর্ব (১)
The given sequence consists of $3$ distinct sequences,namely $(0,10,20,...),(1,11,21,...),(2,12,22,...)$. So $50$th term of the given sequence will be the $17$th term of the second sequence here and it is $161$.
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with-}} \color{green}{\textit{AVADA KEDAVRA!}}$
Re: ২০১৩ এর প্রস্তুতি পর্ব (১)
আমিও প্রথমে 161 বের করেছিলাম। পরে গুগল করে দেখি 0,1,2,10,11,12,20...এই ধারাটা আসলে base 3 ধরে 0,1,2,3,4,5,6,...অর্থাত্ ডেসিমেলের অনুরূপ। ফলে (49)10 কে base 3 তে কনভার্ট করতে হবে।
Re: ২০১৩ এর প্রস্তুতি পর্ব (১)
Now,if you consider it from this point of view,the answer will be $1211$. But where is the problem in your first solution? For example,if I tell you to calculate the next term of the sequence $1,2,4,8,16,...$ what will your answer be? $32$ ? Check the following:simu wrote:আমিও প্রথমে 161 বের করেছিলাম। পরে গুগল করে দেখি 0,1,2,10,11,12,20...এই ধারাটা আসলে base 3 ধরে 0,1,2,3,4,5,6,...অর্থাত্ ডেসিমেলের অনুরূপ। ফলে (49)10 কে base 3 তে কনভার্ট করতে হবে।
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with-}} \color{green}{\textit{AVADA KEDAVRA!}}$
- Fahim Shahriar
- Posts:138
- Joined:Sun Dec 18, 2011 12:53 pm
(Base 3)
$49/3$ ; Remainder 1, Quotient 16
$16/3$ ; Remainder 1, Quotient 5
$5/3$ ; Remainder 2, Quotient 1
$1/3$ ; Remainder 1
So the 50th term in (base 3) is $1211$.
$16/3$ ; Remainder 1, Quotient 5
$5/3$ ; Remainder 2, Quotient 1
$1/3$ ; Remainder 1
So the 50th term in (base 3) is $1211$.
Name: Fahim Shahriar Shakkhor
Notre Dame College
Notre Dame College
- nafistiham
- Posts:829
- Joined:Mon Oct 17, 2011 3:56 pm
- Location:24.758613,90.400161
- Contact:
Re: ২০১৩ এর প্রস্তুতি পর্ব (১)
I suggest that, any sequence depends only what is given.
suppose, I give you $1$
what is next ?
$2$ ? $3$ ? $4$ ? $11$ ? $10$ ?
each and every has some logic behind it.
Of course it is true that just $1$ can't be a sequence or series,
what I want to say is any logic that satisfies what is given should be right.
None can claim none.
As much as I know when such series are given, they try to find all possible logics, or try to give something that can have only one answer.
suppose, I give you $1$
what is next ?
$2$ ? $3$ ? $4$ ? $11$ ? $10$ ?
each and every has some logic behind it.
Of course it is true that just $1$ can't be a sequence or series,
what I want to say is any logic that satisfies what is given should be right.
None can claim none.
As much as I know when such series are given, they try to find all possible logics, or try to give something that can have only one answer.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Re: ২০১৩ এর প্রস্তুতি পর্ব (১)
The very thing I wanted to tell.nafistiham wrote:what I want to say is any logic that satisfies what is given should be right.
As much as I know when such series are given, they try to find all possible logics, or try to give something that can have only one answer.
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with-}} \color{green}{\textit{AVADA KEDAVRA!}}$
- Phlembac Adib Hasan
- Posts:1016
- Joined:Tue Nov 22, 2011 7:49 pm
- Location:127.0.0.1
- Contact:
Re: ২০১৩ এর প্রস্তুতি পর্ব (১)
তিহাম ভাইয়ার সাথে আমিও একমত। এই সিরিজকে একমুখী করার জন্য অন্তত আরও তিনটি টার্ম দেওয়া উচিত ছিল। তাহলে বোঝা যেত যে এতে $22$এর পরে $30$ না এসে $100$ আসছে। তখন হয়ত বিষয়টি অন্যরকম হত।
Welcome to BdMO Online Forum. Check out Forum Guides & Rules
Re: ২০১৩ এর প্রস্তুতি পর্ব (১)
অথবা ইন্টারপোলেশন মাইরা একটা polynomial আনা যায়nafistiham wrote:I suggest that, any sequence depends only what is given.
suppose, I give you $1$
what is next ?
$2$ ? $3$ ? $4$ ? $11$ ? $10$ ?
Please read Forum Guide and Rules before you post.
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
Re: ২০১৩ এর প্রস্তুতি পর্ব (১)
Answer is maybe $1001$.