PYTHON. That is just the way the pattern is

1.Write a recursive function printPattern() that will generate the following patterns. Note that the first argument is always a power of 2 and is the max number of stars appearing in the middle row. The second argument (which defaults to 0) is the number of spaces to put before each patterns rows of stars.

>>> printPattern(8,0)

*

**

*

****

*

**

*

********

*

**

*

****

*

**

*

>>> printPattern(4,2)

*

**

*

****

*

**

*

>>> printPattern(4)

*

**

*

****

*

**

*

2. Write a recursive function gcd(m,n) that returns the greatest common divisor of a pair of numbers. The gcd of m and n is the largest number that divides both m and n. If one of the numbers is 0, then the gcd is the other number. If m is greater than or equal to n, then the gcd of m and n is the same as the gcd of n and m-n. If n is greater than m, then the gcd is the same as the gcd of m and n-m.

>>> gcd(5,0)

5

>>> gcd(15,5)

5

>>> gcd(5,7)

1

>>> gcd(24,144)

24

>>> gcd(124,144)

4

>>>

3. Write a recursive function f that generates the sequence 0,1,0.5,0.75,0.625,0.6875,0.65625,0.671875,0.6640625,0.66796875. The first two terms are 0 and 1, every other term is the average of the two previous.

>>> f(0)

0

>>> f(1)

1

>>> f(2)

0.5

>>> [ (i,f(i)) for i in range(10)]

[(0, 0), (1, 1), (2, 0.5), (3, 0.75), (4, 0.625), (5, 0.6875), (6, 0.65625), (7, 0.671875), (8, 0.6640625), (9, 0.66796875)]

>>>