Just 9 around

Algebra Level 3

If the arithmetic mean of nine numbers in the given set { 9 , 99 , 999 , 9999 , . . . . . , 999999999 } \{9,99,999,9999,.....,999999999\} is a nine digit number N N , then N N doesn't contain

9 0 6 None of these 1

Tanishq Varshney by Tanishq Varshney , 23, India

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1 solution

Tanishq Varshney
Nov 11, 2015

9 + 99 + 999 + . . . . + 999999999 9 \large{\frac{9+99+999+....+999999999}{9}}

9 ( 1 + 11 + 111 + . . . . + 111111111 ) 9 \large{\frac{9(1+11+111+....+111111111)}{9}}

123456789 \large{\boxed{123456789}}

Hence it doesn't contain 0.

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