Find the number of natural numbers which are less than `2xx10^8` and which can be written by means of the digit 1 and 2.

Answer

766

Explanation

Number of 1 digit number =2
Number of 2 digit number `=2xx2=2^(2)`
Number of 3 digit number `=2xx2xx2=2^(3)`
Number of 8 digit number `=2xx2xx..xx2=2^(8)`
Number of 9 digit number `=1xx2xx2xx..xx2(8"times")=2^(8)`
`therefore` Total numbers`=2+2^(2)+2^(3)+..+2^(8)+2&(9)`
` =(2(2^(8)-1))/(2-1)+2^(8)=2^(9)-2+2^(8)=766`