BdMO National Higher Secondary 2010/3

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BdMO
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BdMO National Higher Secondary 2010/3

Unread post by BdMO » Mon Feb 07, 2011 12:07 am

Problem 3:
A series is formed in the following manner:
$A(1)=1$
$A(n)=f(m)$ numbers of $f(m)$ followed by $f(m)$ numbers of $0$.
$m$ is the number of digits in $A(n-1)$.
Find $A(30)$. Here $f(m)$ is the remainder when $m$ is divided by $9$.

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nafistiham
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Re: BdMO National Higher Secondary 2010/3

Unread post by nafistiham » Tue Jan 10, 2012 5:56 pm

following the rules we can get some $A$s easily
like
$A(1)=1$
$A(2)=10$
$A(3)=2200$
$A(4)=44440000$
$A(5)=8888888800000000$
$A(6)=77777770000000$
$A(7)=5555500000$
$A(8)=10$
so, it is gona repeat.and....
\[A(30)=77777770000000\]
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
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