Solve the following equation :
\[\frac{2}{3}\left [ 1+\frac{1}{1+x} +\frac{1}{(1+x)^3}+\frac{1}{(1+x)^5 }+\cdot \cdot \cdot\right ]=1\]
BdMO 2004 Secondary - 2(b)
- 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.
Re: BdMO 2004 Secondary - 2(b)
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
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
- nafistiham
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Re: BdMO 2004 Secondary - 2(b)
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
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.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Re: BdMO 2004 Secondary - 2(b)
my mistake. my answer is also \[\pm\] \[x=\sqrt2\]
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Re: BdMO 2004 Secondary - 2(b)
Solved
here.
here.