Python palindrome program w/o string functions

I'm a beginner in Python. I've written palindrome programs without using string functions.

Question 1: Why does the 1st logic not give me the desired output? Correct me if I'm wrong.

Question 2: In the 2nd program if I skip i += 1 in if statement it should give me the correct result as the for loop automatically increments value of i. Rather it gives me correct output only if I include that statement or else not. What may be the reason for this?

Logic 1:

n = input("eNTER  STRING\n")
length = int(len(n))
n = str(n)

for i in range(0, int(length/2+1)):
   if n[i] != n[-i - 1]:
      break

if i < int(length/2 + 1):
   print("not")
else:
   print("yes")

Logic 2:

n = input("ENTER  STRING\n")
length = int(len(n))

for i in range(0, int(length/2 + 1)):
   if n[i] == n[-i - 1]:
      i += 1
   else:
      break

if i < (length / 2):
   print("not")
else:
   print("yes")

Thanks in advance..

In Logic 1, try if i<int(length/2): instead of if i<int((length/2+1)):

In Logic 2, even removing i+=1 gives the correct result:

if n[i] == n[-i-1]:
    pass
else:
    break

You can also use the following code for the same:

def reverse(text):
    if len(text) <= 1:
        return text
    return reverse(text[1:]) + text[0]

n = input("ENTER  STRING\n")
if n==reverse(n):
    print ("It's a palindrome")
else:
    print ("It's not a palindrome")