created 08/04/99

# 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.

## 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.
```

## 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

*******
******
*****
****
***
**
*
```

## Exercise 4 --- Pine Tree

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

```       *
***
*****
*******
*********
***********
*************
***************
***
***
***
```