We need to find the value of lim n--> inf [ bn/2^n]

Also, we have bn = 1 + 2 + 2^n

lim n--> inf [ bn/2^n]

=> lim n--> inf [(1 + 2 + 2^n)/2^n]

=> lim n--> inf [1/2^n + 2/2^n + 2^n/2^n]

for n--> inf , we have 2^n --> inf and (1/2^n) --> 0

lim n--> inf [1/2^n + 2/2^n + 2^n/2^n]

=> 0 + 0 + 1

**The required limit = 1**

[This answer is the solution to the unedited question.]