Arithmetic mean of nine numbers in given set {9,99,999,...., 999999999} is a 9 digit number N , all

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8. Sequences and Series

normal

The arithmetic mean of the nine numbers in the given set $\{9,99,999,...., 999999999\}$ is a $9$ digit number $N$, all whose digits are distinct. The number $N$ does not contain the digit

A

$0$

B

$2$

C

$5$

D

$9$

Solution

$A=\frac{9+99+999+\ldots .+999999999}{9}$

$\Rightarrow A=1+11+111+\ldots+111111111$

$\Rightarrow \mathrm{A}=123456789 \quad$ (doesn't contain zero)

Standard 11

Mathematics

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