A palindrome is a string whose reversal is identical to the string. How many bit strings of length n are palindromes?

The number of  palindromes is  

      when n is even and

      when n is odd

Step-by-step explanation:

From the question we are told that

    The  length of the string is  

Generally palindrome is evaluated by considering the first part of a string

  When the the length of the string is an even number then

it means that the first part of the string is

Hence the number of  bit strings of length n that are  palindromes is evaluated as

But When the the length of the string is an odd number then

it means that the first part of the string is

Hence the number of  bit strings of length n that are  palindromes is evaluated as

Generally each bit could be either 0 or  1

Hence the number of  palindromes is  

      when n is even and

       when n is odd

the image is given below

since the options are not given so we draw it from the equation

the given equation is

y = (x-1) (x+4)

y = y² + 3x - 4

the above equation is a quadratic equation which will have two roots. if we draw the graph for it, it will look like this