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 $9$.
BdMO National Higher Secondary 2010/3
- 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....
\[A(30)=77777770000000\]
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.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.