1. In the first loop 
      n = 0
      c = 1 + 1 = 2
      b = 1
      a = 2
   
   In the second loop
      n = 1
      c = 1 + 2 = 3
      b = 2
      a = 3

   In the throed loop
      n = 2
      c = 2 + 3 = 5
      b = 3
      a = 5

   n++ (3) and it violates the condition n < 3. The 
   loop terminates.

   The output is 
   a = 5
   b = 3

2. This program does not initialize sum. You will receive a
   error message when compiling. Another problem
   is that if you set sum 0 the result of the program will be 0
   but not the desired result 30.

3.   public static int prod(int n)
     {
        if (n == 1)
           return 1;
        return prod(n-1) * (2*n-1);
     }
 

4. The while version:

   public static int prod(int n)
   {
       int i = 1;
       int r = 1;
       while (i <= n)
       {
           r = r * (2*i-1);
           i ++;
       }
       return r;
   }


   The for version:
   
   public static int prod(int n)
   {
      int r = 1;
      for (int i = 1; i <= n; i ++)
         r = r * (2*n-1);

      return r;
   }

5.
    public class ProcessData {
        public static main(String[] args)
        {
             int n = 0;
             double sum;
             double max = Double.NEGATIVE_INFINITY;
             while (!StdIn.isEmpty()) 
             {
                int a = StdIn.readInt();
                double b = stdIn.readDouble();
                if (a > 0) 
                {
                   n++;
                   sum += a;
                }
                
                if (b > max) 
                   max = b;
             }

             Systme.out.println("Average= " + sum/n);
             System.out.println("Max= " + max);
        }
    } 
 
6.
   public static boolean hasAllCharacters(String a, String b)
   {
       for (int i = 0; i < b.length(); i ++)
       for (int j = 0; j < a.length(); j ++)
       {
           if (b.charAt(i) != a.charAt(j)) 
               return false;
       }

       return true;
   }


7.
   public static boolean isEmbeddedString(String a, String b)
   {
       if (a.length() == 0) return true;
       if (b.length() == 0) return false;
       
       if (a.charAt(0) == b.charAt(0))
          return isEmbeddedString(a.substring(1), b.substring(1));
       else
          return isEmbeddedString(a, b.substring(1));
   }