Exercise-1.14(new book) (BOMC-2011)
Can anyone explain this problem. I can't understand the phrase " the fractional part".
Prove that for any positive integer n, the fractional part of \[\sqrt{4n^2+n}\]
is smaller than\[\frac{1}{4}\]
Prove that for any positive integer n, the fractional part of \[\sqrt{4n^2+n}\]
is smaller than\[\frac{1}{4}\]
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.........
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Re: Exercise-1.14(new book) (BOMC-2011)
Fractional part of ($\sqrt 2 = 1.414...$) is ($.414...$)
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: Exercise-1.14(new book) (BOMC-2011)
many many thanks Sourav da.
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.........
Re: Exercise-1.14(new book) (BOMC-2011)
need hints(the more the better;coz it seems a bit difficult!)
r@k€€/|/
Re: Exercise-1.14(new book) (BOMC-2011)
Try finding a perfect square just greater than $4n^2+n$.
Last edited by *Mahi* on Mon Oct 31, 2011 8:13 pm, edited 1 time in total.
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Re: Exercise-1.14(new book) (BOMC-2011)
Or just less than $4n^2 + n$
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: Exercise-1.14(new book) (BOMC-2011)
Nope, the problem says the fractional part smaller than $\frac 1 4$sourav das wrote:Or just less than $4n^2 + n$
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Re: Exercise-1.14(new book) (BOMC-2011)
like $9n^{2}$ ?*Mahi* wrote:Try finding a square integer just greater than $4n^2+n$.
as $\sqrt{9n^{2}}=3n $ ???
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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: Exercise-1.14(new book) (BOMC-2011)
No, something greater than $4n^2+n$ which you can express as perfect square.
Last edited by *Mahi* on Mon Oct 31, 2011 8:17 pm, edited 1 time in total.
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Re: Exercise-1.14(new book) (BOMC-2011)
Any of them will work. See:*Mahi* wrote:Nope, the problem says the fractional part smaller than $\frac 1 4$sourav das wrote:Or just less than $4n^2 + n$
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......(-$from$ "$THE$ $UGLY$ $TRUTH$" )