Ytukyg

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Whatever I enter between -1 and 1, the outputs are always 1.0000 or 2.0000. How can I do solve this problem? Below I attached my code.

#include <stdio.h>

#include <math.h>





int main() {



    int i;

    float x;

    float sum=0;





    printf ("enter an xn");

    scanf ("%f",&x);



    if ((x>-1)&&(x<1))

    {

         for (i=0;i<101;i++)

         sum= sum + (pow(x,i));

    }    



    printf ("result=%f",sum);

    return 0;

}

Even using a type like double you haven't enough numerical precision to sum all the powers up to 100.

Executing the following snippet, you'll notice that, while the corret (numerically speaking) result is evaluated, the loop stops way before the 100th iteration, tipically at 16:

#include <stdio.h>

#include <math.h>

#include <float.h>



// Analitically calculates the limit for n -> inf of the series of powers

double sum_of_powers_limit(double x)

{

    return 1.0 / (1.0 - x);

}



int main(void)

{

    double x = 0.1;

    const int N = 100;

    double sum = 1.0;



    for (int i = 1; i <= N; ++i)

    {

        double old_sum = sum;

        sum = sum + pow(x,i);



        if (old_sum == sum)

        {

            fprintf(stderr, "Numerical precision limit reached at i = %dn", i);

            break;

        }

    }



    printf("  result = %.*en", DBL_DECIMAL_DIG, sum);

    printf("expected = %.*en", DBL_DECIMAL_DIG, sum_of_powers_limit(x));



    return 0;

}

Also note that a more efficient way to evaluate this kind of polynomials is the Horner's method:

// Evaluates the sum s(x) = 1 + x + x^2 + ... + x^n using Horner's method

// It stops when it cannot update the value anymore

double sum_of_powers(double x, int n)

{

    double result = 1.0;

    for (int i = 0; i < n; ++i)

    {

        double old_result = result;

        result = 1.0 + x * result;



        if (old_result == result)

        {

            fprintf(stderr, "Numerical precision limit reached at i = %dn", i);

            break;

        }

    }

    return result;

}

if ((x>-1)&&(x<1))
With this case your code will work only if x is zero so try removing if statement and do mention what output you expect for given particular input, it will be bit more helpful to answer it.

Try this code:

#include <stdio.h> 

#include <math.h> 

int main() { 

    int i; float x; 

    float sum=0; 



    printf ("enter an xn"); 

    scanf ("%f",&x); 

    for (i=0 ;i<101; i++) 

        sum+= (pow(x,i)); 



    printf ("result=%f",sum); 

    return 0;

}