Having problems generating a star pattern in python suggested from a book but getting different results

I am new on Python and I am following a book that purposes the following excercise:

Write a program to generate the following pattern in Python:

*
**
***
****

The suggested code is:

n = input('Enter the number of rows: ')
m = int(n)
*k = 1
for i in range(m):
    for j in range(i, i + 2):
        print('*', end = " ")
    print()

and enter n=5.This lead me to ask to questions. The first one is the *k=1, I am asumming the '' is a typo on the book since my program does not run with it. However i am not seeing that k is being used within the loop. My second question is that I do not understand why my outcome is different than the one I get (once removed the ''). This is what I get when n=5:

**
**
**
**
**