$2^{100}$
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Phlembac Adib Hasan
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Here I'm giving a well-known problem.Actually it's for them who have not solved yet.Just find how many digits $2^{100}$ has if it is written in decimal numeric system.(and part b- can you generalize this?)
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Re: $2^{100}$
This is not an secondary level problem(in my opinion) and junior level students should know it. So moving it to junior level.
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Nur Muhammad Shafiullah | Mahi
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Re: $2^{100}$
Do junior level students know about logarithms and power series?
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Re: $2^{100}$
I learnt them 2 years ago at PMS :S
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Re: $2^{100}$
I don't think everyone goes to PMS.
"Everything should be made as simple as possible, but not simpler." - Albert Einstein
Re: $2^{100}$
Then forum can be substitute to PMS! The junior can learn that now 
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Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
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Re: $2^{100}$
Then maybe explain your solution to the juniors, otherwise how will they use something they never even heard of? I don't think I heard of these terms when I was a junior.
"Everything should be made as simple as possible, but not simpler." - Albert Einstein
Re: $2^{100}$
But I really think junior students nowadays knows basic logarithm well. At least they understand that all integers greater than or equal to $10^k$ and less than $10^{k+1}$ have $k+1$ digits. That is all logarithm needed for this problem, and BdMO in recent years have this kind of problems quite much. This might be quite hard for class VI students , but students of class VIII may know it well.
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nafistiham
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Re: $2^{100}$
two years ago, even you were in class $IX$[color=#00BF00]*Mahi*[/color] wrote:I learnt them 2 years ago at PMS :S
my goodness.i learned it just now.see, if i am doing it right.[color=#00BF00]*Mahi*[/color] wrote:all integers greater than or equal to $10^k$ and less than $10^{k+1}$ have k digits.
$10^1<31<10^2$ if i am counting right i see there is $2$ digits in $31$ where $k=1$ in this case $31$ has $k+1$ digits.i think it should have been $k+1$.
and, does dkaka parallel math school exist ? I didn't know
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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: $2^{100}$
1.It was about two and a half years ago, when I was in class VIII.
2. Very lame typo, fixed.
And yes,there is Ramanujan Gonit Songho in Dhaka.
2. Very lame typo, fixed.
And yes,there is Ramanujan Gonit Songho in Dhaka.
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