Programming Exercises¶

1. Write a recursive program to compute the sum of the first n numbers

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   (ex_rec_1)

2. Write a recursive program to compute the pow of a number.

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   (ex_rec_2)

3. Pascal’s triangle is a number triangle with numbers arranged in staggered rows such that

   \[a_{nr} = {n! \over{r! (n-r)!}}\]

   This equation is the equation for a binomial coefficient. You can build Pascal’s triangle by adding the two numbers that are diagonally above a number in the triangle. An example of Pascal’s triangle is shown below.

           1
         1   1
       1   2   1
     1   3   3   1
   1   4   6   4   1
   

   Write a program that prints out Pascal’s triangle. Your program should accept a parameter that tells how many rows of the triangle to print.

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   (ex_rec_13)