Let $S(x)$ be the sum of the digits of the positive integer $x$ in its decimal
representation.
(a) Prove that for every positive integer $x$,
$\frac{S(x)}{S(2x)}\leq 5$ Can this bound be
improved?
(b) Prove that $\frac{S(x)}{S(3x)}$is not bounded.
Advance P-2(BOMC-2)
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You spin my head right round right round,
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
Re: Advance P-2(BOMC-2)
Posting only the hints again. Do not open them all at once. Do it serially .This is because it is easier to get the later hints when you know the earlier ones.
Warning: My solution is too much abstract :S I think I should see the official solution as well.
First and basic:
Then:
Desperate:
Warning: My solution is too much abstract :S I think I should see the official solution as well.
First and basic:
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- nafistiham
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Re: Advance P-2(BOMC-2)
what is meant by can this bound be improved ?
does it mean whether it can be shown or not that there can be a greater value than $5$ ?
if it is then
does it mean whether it can be shown or not that there can be a greater value than $5$ ?
if it is then
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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Re: Advance P-2(BOMC-2)
It is actually "a smaller value than $5$".nafistiham wrote:what is meant by can this bound be improved ?
does it mean whether it can be shown or not that there can be a greater value than $5$ ?
if it is then
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- nafistiham
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Re: Advance P-2(BOMC-2)
but, $\frac {5}{1}=5$ where, $x=5$ and $2x=10$ so it cant be improved, right ?
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
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Re: Advance P-2(BOMC-2)
Yes, that's right.
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Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
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