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### code for a function S(x) of calculating the sum of a series with a given accuracy in language C

Here is an example code in C to calculate the sum of a series with a given accuracy:

c`#include <stdio.h> #include <math.h> double S(double x, double accuracy); int main() { double x, accuracy; printf("Enter the value of x: "); scanf("%lf", &x); printf("Enter the desired accuracy: "); scanf("%lf", &accuracy); double sum = S(x, accuracy); printf("The sum of the series is: %lf\n", sum); return 0; } double S(double x, double accuracy) { double sum = 0, term = 1, i = 1; while (fabs(term) >= accuracy) { sum += term; i++; term = -term * x / i; } return sum; }`

The `S()`

function takes two arguments: the value of `x`

and the desired accuracy `accuracy`

. It initializes the variables `sum`

, `term`

, and `i`

to zero, one, and one, respectively. It then enters a `while`

loop that continues until the absolute value of `term`

is less than `accuracy`

. Inside the loop, it adds `term`

to `sum`

, increments `i`

, and calculates the next term using the formula `-term * x / i`

. The function returns the final value of `sum`

.

In the `main()`

function, the user is prompted to enter the values of `x`

and `accuracy`

. The function `S()`

is then called with these values, and the resulting sum is printed to the console.

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C Program To Find Sum of Series 1/1! + 2/2! + 3/3! + …. + n/n!

### How to find the sum of a series in C?

To find the sum of a series in C, you can use a loop to iterate through the terms of the series and add them together. Here’s an example of how to do this:

c`#include <stdio.h> int main() { int n; double sum = 0.0; printf("Enter the number of terms in the series: "); scanf("%d", &n); for (int i = 1; i <= n; i++) { sum += 1.0 / i; // Add the ith term to the sum } printf("The sum of the series is: %lf", sum); return 0; }`

In this example, we use a `for`

loop to iterate through the terms of the series from 1 to `n`

, where `n`

is the number of terms in the series. Inside the loop, we add the ith term to the `sum`

variable using the formula for the series. Finally, we print out the value of `sum`

.

Note that the above example assumes that you know the formula for the series you are trying to sum. If you don’t know the formula, you will need to find it before you can write a program to compute the sum.

### How to code series in C?

In C, you can code a series using loops and variables to store and manipulate values in the series. Here is an example code for generating and printing a series of numbers:

c`#include <stdio.h> int main() { int n = 10; // The number of terms in the series int i, term = 1; // i is the loop variable, term is the current term in the series // Loop for generating and printing the series for (i = 0; i < n; i++) { printf("%d ", term); // Print the current term term = term + 2; // Update the current term for the next iteration } return 0; }`

In this example, we are generating a series of even numbers. We initialize the loop variable `i`

to zero, and the current term in the series `term`

to 1. We then use a `for`

loop to iterate `n`

times, printing out the current value of `term`

each time, and updating `term`

by adding 2 to it. Finally, we return 0 to indicate successful completion of the program.

You can modify this code to generate and print different series depending on the pattern you want to follow.

### How to calculate sum of digits of a number using while loop in C?

Here’s an example program in C to calculate the sum of digits of a given number using a while loop:

c`#include <stdio.h> int main() { int num, sum = 0; printf("Enter a number: "); scanf("%d", &num); while (num > 0) { sum += num % 10; // add the last digit to sum num /= 10; // remove the last digit from num } printf("Sum of digits: %d\n", sum); return 0; }`

Here’s how the program works:

- We declare two variables
`num`

and`sum`

.`num`

is the number whose digits we want to sum, and`sum`

will hold the sum of the digits. - We prompt the user to enter a number using
`printf`

and read it using`scanf`

. - We start a while loop that will run as long as
`num`

is greater than 0. Inside the loop:- We use the modulus operator
`%`

to get the last digit of`num`

and add it to`sum`

. - We divide
`num`

by 10 to remove the last digit. For example, if`num`

is 123,`num /= 10`

will set`num`

to 12.

- We use the modulus operator
- Once the loop is done, we print the sum of digits using
`printf`

. - Finally, we return 0 to indicate that the program has run successfully.

For example, if the user enters 1234, the output will be:

yaml`Enter a number: 1234 Sum of digits: 10`

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