Find the Sum of the Series: 1/1! + 1/2! + 1/3! + … + 1/n! using JavaScript ?

We are going to discuss how we can find the sum of series: 1/1! + 1/2! + 1/3! + …… till n terms.

Below are the approaches to find the sum of series:

Using for loop

We will first define a function to calculate factorial of a given number. It checks if the number is 0 or 1 it returns 1 else, it recursively calculates factorial. Now we define another function and initialize a variable sum to 0. Use a for loop to iterate from 1 to n. For each iteration, calculate the reciprocal of the factorial of the current number i and add it to the sum. Return sum.

Example: To demonstrate calculation of sum of given series using for loop

JavaScript

// Using for loop

function factorial(num) {
    if (num === 0 || num === 1) {
        return 1;
    } else {
        return num * factorial(num - 1);
    }
}

function sumSeries(n) {
    let sum = 0;
    for (let i = 1; i <= n; i++) {
        sum += 1 / factorial(i);
    }
    return sum;
}

console.log(sumSeries(3)); 

Output

1.6666666666666667

Time Complexity: O(n)

Space Complexity: O(n)

Using Recursion

We will first define a function to calculate factorial of a given number. It checks if the number is 0 or 1 it returns 1 else, it recursively calculates factorial. We will create another recursive function. The base case of this recursive function is : If n is 1, return 1. Else, calculate the reciprocal of the factorial of n and add it to the result of recursively calling the function with n – 1.

Example: To demonstrate calculation of sum of given series using recursion.

JavaScript

// Using recursion

function factorial(num) {
    if (num === 0 || num === 1) {
        return 1;
    } else {
        return num * factorial(num - 1);
    }
}

function sumSeries(n) {
    if (n === 1) {
        return 1;
    }
    return 1 / factorial(n) + sumSeries(n - 1);
}


console.log(sumSeries(3)); 

Output

1.6666666666666667

Time Complexity: O(n)

Space Complexity: O(n)