China-1990-1

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sm.joty
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China-1990-1

Unread post by sm.joty » Sun Apr 01, 2012 2:40 pm

Let $a,b$ positive real numbers and $a+b=2$.What is the minimum and maximum value of $\frac{1}{1+a^n}+\frac{1}{1+b^n}$
for any positive integer $n$ :)

Edited
Last edited by sm.joty on Mon Apr 02, 2012 1:07 pm, edited 1 time in total.
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Niloy Da Fermat
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Re: China-1990-1

Unread post by Niloy Da Fermat » Sun Apr 01, 2012 3:44 pm

sm.joty wrote:Let $a,b$ positive integers and $a+b=2$.What is the minimum and maximum value of $\frac{1}{1+a^n}+\frac{1}{1+b^n}$
for any positive integer $n$ :)
are your infos correct?you know, what is meant by $ a,b $ positive integers and $ a+b=2 $ :P
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nafistiham
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Re: China-1990-1

Unread post by nafistiham » Sun Apr 01, 2012 9:04 pm

According to the problem the solution is $\frac {1}{4}$ as $a=b=1$
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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Sazid Akhter Turzo
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Re: China-1990-1

Unread post by Sazid Akhter Turzo » Sun Apr 01, 2012 11:26 pm

@sm.joty vaia,
There must be a problem in your problem. So, please correct it.
Turzo

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sm.joty
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Re: China-1990-1

Unread post by sm.joty » Mon Apr 02, 2012 1:11 pm

Sazid Akhter Turzo wrote:@sm.joty vaia,
There must be a problem in your problem. So, please correct it.
Turzo
are your infos correct?you know, what is meant by $a,b$ positive integers and $a+b=2$
Very sorry for my Typo :oops:
This mistake occur because most of the problem related to integers.so....... :)
Then I think now the problem is ok. :)
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