Problem 1: I need to use induction to prove that the number of binary strings of length n equals 2^n.
Problem 2. Number of binary strings of length at most n equals 2^(n+1) -1
Problem 3. for every integer n > 0 or n = 0 there are integers a and b such that 2a + 3b = n.
Can somebody help me out on these 3 problems, they are my last posts as i finish my course tomorrow! It be great help if you guys can show me these 3 questions cause they will be in exam i bet!
For (1), if n= 1 the only binary strings of length 1 are "0" and "1" so there are .
Assume that for some k, the number of binary strings of length k is . From each of those, you can create a new string of length k+1 by appending either a "0" or a "1"- so you can create 2 new strings of length k+1 from each string of length k.
For (2), The number of strings of length less than or equal to k+1 is the number of strings of length less than or equal to k plus the number of strings of length k+1.