BdMO 2004 Secondary - 2(b)

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
User avatar
nafistiham
Posts:829
Joined:Mon Oct 17, 2011 3:56 pm
Location:24.758613,90.400161
Contact:
BdMO 2004 Secondary - 2(b)

Unread post by nafistiham » Mon Jan 09, 2012 9:44 pm

Solve the following equation :
\[\frac{2}{3}\left [ 1+\frac{1}{1+x} +\frac{1}{(1+x)^3}+\frac{1}{(1+x)^5 }+\cdot \cdot \cdot\right ]=1\]
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Introduction:
Nafis Tiham
CSE Dept. SUST -HSC 14'
http://www.facebook.com/nafistiham
nafistiham@gmail

protik
Posts:35
Joined:Wed Dec 08, 2010 7:21 am

Re: BdMO 2004 Secondary - 2(b)

Unread post by protik » Mon Jan 09, 2012 10:13 pm

I can't write latex well. so I am giving short solution with banglish.( can't know the english of some word)
bracket ar vitorer ongshe osim gunnottor dharar sutro proyog korle :
3(X^2+2X) = 2(1+2X+X^2)
and ata solve korle
X = -(1+root3) or root3 -1 answer ase
If i haven't done any mistake :)

User avatar
nafistiham
Posts:829
Joined:Mon Oct 17, 2011 3:56 pm
Location:24.758613,90.400161
Contact:

Re: BdMO 2004 Secondary - 2(b)

Unread post by nafistiham » Mon Jan 09, 2012 10:41 pm

notice that the sequence inside the bracket is not a geometric sequence unless you cut out $1$ from it. :)
now do it in the same way. if my calculation is not wrong
\[x=\pm\sqrt2\]

*edited.courtesy:protik
Last edited by nafistiham on Wed Jan 11, 2012 3:01 pm, edited 1 time in total.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Introduction:
Nafis Tiham
CSE Dept. SUST -HSC 14'
http://www.facebook.com/nafistiham
nafistiham@gmail

protik
Posts:35
Joined:Wed Dec 08, 2010 7:21 am

Re: BdMO 2004 Secondary - 2(b)

Unread post by protik » Tue Jan 10, 2012 10:55 pm

my mistake. my answer is also \[\pm\] \[x=\sqrt2\]

samiul_samin
Posts:1007
Joined:Sat Dec 09, 2017 1:32 pm

Re: BdMO 2004 Secondary - 2(b)

Unread post by samiul_samin » Tue Feb 26, 2019 6:25 pm

Solved

here
.

Post Reply