Chapter 17 Programming Exercises

Exercise 1 --- Adding up Squares and Cubes

Write a program that adds up the squares and adds up the cubes of integers from 1 to N, where N is entered by the user:

Upper Limit:
5
The sum of Squares is  55
The sum of Cubes   is  225

Do this by using just one loop that generates the integers. Of course, if you really needed to calculate these sums you would use the appropriate formulas:

12 + 22 + 32 + ... + n2 = n(n+1)(2n+1)/6

13 + 23 + 33 + ... + n3 = n2(n+1)2/4

Add these formulas to your program and print out their results as well as that of the explicit summations.

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Exercise 2 --- Power of a number

Write a program that computes XN where X is a floating point number and N is a positive integer. The program informs the user that N must be positive if the user enters a negative value. Of course,

XN = X * X * X * ... * X   
     --------------------
           N times

The user dialog will look something like this:

Enter X
1.3
Enter N
5

1.3 raised to the power 5 is:  3.71293

-------

Enter X
5.6
Enter N
-3

N must be a positive integer.

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Exercise 3 --- Wedge of Stars

Write a program that writes a wedge of stars. The user enters the initial number of stars, and the program writes out lines of stars. Each line has one few star than the previous line:

Initial number of stars:
7

*******
******
*****
****
***
**
*

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Exercise 4 --- Pine Tree

Write a program that writes a tree made of stars on the terminal:

       *
      ***
     *****
    *******
   *********
  ***********
 *************
***************
      ***
      ***
      ***

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