Thread: Maclaurins Series

Whats wrong with the following code to find maclaurin series?

Code:

#include <stdio.h>
#include <math.h>
#define TRUE 1
#define FALSE 0

int main ()
{
    int x, n, i;
         double approx = 0;
	/* Write your code here */
	scanf("%d", &x);
       scanf("%d", &n);
       printf("%d", x);
       printf("%d", n);
       while (n <= 1)
 {   approx = pow(x, n);
      approx += approx;
      n++;
}	
while ( n > 1)
  {   		i = n;
        	while ( i > 0)
        {
           approx = (pow(x, n) * 1.0) / (i);
           approx += approx;
        	i--;
}     
     
}
printf("%.10lf\n", approx);
return 0;
}

Ok, from a very quick initial look here are potential problems I've found.

1) I am assuming that the variable 'n' refers to the degree you want to take the Maclaurin Series to (i.e. the level of the approximation. As n -> infinity, the error tends to zero). In that case, why is it that if you put in a value for n which is anything other than 0 or 1 the first while loop is completely skipped? What is the point in that?

i.e. This line of code is questionable

Code:

while(n <= 1 )

2) Even more interestingly, in the second loop you have two loops inside one another and for the terminating condition of the first loop you have n > 1 although no 'n--' statement anywhere in either loop - How exactly does the loop ever terminate if it is initially executed?

3) In the central loop you have these two lines:

Code:

approx = (pow(x, n) * 1.0) / (i);
approx += approx;

That is completely equivilent to this line of code:

Code:

approx = 2*pow(x,n)/i;

Because you are saying approx = [some crap], and then saying approx = approx + [same crap again].

4) By saying approx = [some_number] you complete lose the value it was before which is obviously causing you problems in your program.

5) This isn't a problem, although a remark - Why do you bother having two loops inside each other when one would work fine? It would make things far easier and not to mention easier to write.

6) Again, another remark. Ever thought about doing something like this:

Code:

double FunctionTerm(double x, double n)
{
       /* Function to return the n-th term of a function based on the position, x and the term number */

      /* E.g. for sin(x) this would be something like this */
      double val = 0.0;
      val = (pow(-1, n)/Factorial(2*n+1))*pow(x, 2*n+1);
      return val;
}

int main()
{
       /* Do loop here */
      int i = 0;
      for(i=0; i <=n; i++)
      {
             /* You can do this bit */
      }
     return 0;
}

You would have to write the 'Factorial' function and do all the for loop stuff, but you catch my drift. The reason it is better to structure it like that is that if you want to approximate another function all you have 2 do is change the FunctionTerm function so that it gives the value of each term for a given x and n.

Btw, I'm still not sure what function you were trying to approximate.

Edit: I'm almost certain there are more problems than I've pointed out, but the ones above are the obvious ones.

I know it has already been said, but from now on, please use code tags. lol