## BdMO National Higher Secondary 2010/3

BdMO
Posts: 134
Joined: Tue Jan 18, 2011 1:31 pm

### BdMO National Higher Secondary 2010/3

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 $9$.

nafistiham
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### Re: BdMO National Higher Secondary 2010/3

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.