how many ndigit binary sequences are there without any pair

how many n-digit binary sequences are there without any pair of consecutive digits being the same?

Solution

The nunmber of n-digit binary sequences without any pair of consecutive digits being the same is 2 only.

example : for n = 2

The possible binary sequences are    S₁: 1 0       , S₂: 0 1

for n = 3

The possible binary sequences are    S₁: 1 0 1     , S₂: 0 1 0

for n = 4

The possible binary sequences are    S₁: 1 0 1 0      , S₂: 0 1 0 1

for n = 5

The possible binary sequences are    S₁: 1 0 1 0 1    , S₂: 0 1 0 1 0