Let $0 \leq x,y \leq $1 . Prove that,
\[\frac{1}{\sqrt{1+x^2}} + \frac{1}{\sqrt{1+y^2}} \leq \frac{2}{\sqrt{1+xy}}\]
[Hint : any positive real number can be written as $e^{u}$ for some real number $u$ . You can use this fact without proof. If you can solve the problem without using this hint, then you will get bonus point]
camp exam problem-9
- nafistiham
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\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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.
- nafistiham
- Posts:829
- Joined:Mon Oct 17, 2011 3:56 pm
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Re: camp exam problem-9
does this $e$ means the exponential?
if it is could someone show me the proof of the hint?
i really couldn't understand the whole thing [hint]
if it is could someone show me the proof of the hint?
i really couldn't understand the whole thing [hint]
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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: camp exam problem-9
I think I can solve it. But I always confused about my solution.
And here $e$ is Eular's constant.As a student of secondary (I think), you already know about it. Otherwise follow this link
http://en.wikipedia.org/wiki/E_%28mathe ... onstant%29
Is there any error ?
And here $e$ is Eular's constant.As a student of secondary (I think), you already know about it. Otherwise follow this link
http://en.wikipedia.org/wiki/E_%28mathe ... onstant%29
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