Tag: Natural Logarithm

The Natural Logarithm can be approximated by the following series:

(x – 1 / x) + 1/2 (x – 1 / x)² + 1/2 (x – 1 / x)³ + 1/2 (x – 1 / x)⁴ + ..

If x is input through the keyboard, write a C program to calculate the sum of first seven terms of this series.

Related Read:
For Loop In C Programming Language
Basic Arithmetic Operations In C

Video Tutorial: C Program To Calculate Sum of First 7 Terms of Natural Logarithm

Source Code: C Program To Calculate Sum of First 7 Terms of Natural Logarithm

#include<stdio.h>
#include<math.h>

int main()
{
    int count;
    float x, result = 0.0;

    printf("Enter value of x\n");
    scanf("%f", &x);

    for(count = 1; count <= 7; count++)
    {
        if(count == 1)
        {
            result = (x - 1) / x;
        }
        else
        {
            result = result + pow( (x - 1) / x, count) * 0.5;
        }
    }

    printf("Result of first 7 terms = %0.2f\n", result);

    return 0;
}

Output 1
Enter value of x
5
Result of first 7 terms = 1.98

Output 2
Enter value of x
14
Result of first 7 terms = 3.10

Logic To Calculate Sum of First 7 Terms of Natural Logarithm

According to the problem statement it is clear that we need sum of first 7 terms of Natural Logarithm. So we initialize the loop counter variable count to 1 and iterate through the for loop until count value is less than or equal to 7.

Inside for loop we calculate the value of first 7 terms in the series and store it inside variable result.

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