One can find the sum of n terms of Harmonic Progression using JavaScript. Harmonic Progression is a sequence of real numbers in which each term is reciprocal of Arithmetic Progression.

There are different approaches to finding the sum of n terms of Harmonic Progression which are discussed below:

Using Iteration

In this approach, we will create a function and initialize a variable sum to store the sum of Harmonic Progression. We will use a loop to iterate from 1 to n and in each iteration we will add the reciprocal of the current sum i.e. (we will add 1/i) to the sum. After the loop finishes , we will return the result stored in sum variable.

Example: To demonstrate finding sum of first n terms in the H.P. series using iterative function which uses loop to traverse every element until number of terms reaches to print the result.

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


const n = 7;
const sumOfNTerms = SumOfNTermsHarmonic(n);
console.log(
    `The sum of the first ${n} terms of the H.P. is: ${sumOfNTerms}`);

The sum of the first 7 terms of the H.P. is: 2.5928571428571425

Time Complexity : O(n) , we are using loop

Space Complexity : O(1) , constant space

Using Recursion

In this approach we will define a recursive function. This function stops( i.e. base case) when n is 1 , it will return 1. If n is greater than 1, recursively call the function to calculate the sum of the current term (1/n) and the sum of the previous terms (recursive call with n – 1). Return the result after recursive call stops.

Example: To demonstrate finding sum of first n terms in the G.P. series using recursive function which uses recursive calls till base case reaches to print the result.

function SumOfNTermsHarmonic(n) {

    if (n === 1) {
        return 1;
    } else {

        return 1 / n + SumOfNTermsHarmonic(n - 1);
    }
}
const n = 7;
const sumOfNTerms = SumOfNTermsHarmonic(n);
console.log(
    `The sum of the first ${n} terms of the H.P. is:${sumOfNTerms}`);

The sum of the first 7 terms of the H.P. is:2.5928571428571425

Time Complexity : O(n) , as function make recursive call n times.

Space Complexity : O(n) , n recursive calls are made.

Using Direct Formula

The Sum of first n terms in H.P. is calculated by using the formula for sum of first n terms of H.P. described below :

Syntax:

Sn  = (n/a) + ((n * (n - 1) / 2) * (1 / d)) 

where:

• Sn: is sum of first n terms of H.P.
• n: is number of terms
• a: is first term of H.P.
• d: is common difference of H.P.

Example : To demonstrate finding sum of first n terms in the H.P. series using the function which uses sum of first n terms formula to calculate sum of first n terms of an H.P. series to print the result.

function sumOfFirstNTermsHP(n, a, d) {

    return (n / a) + ((n * (n - 1) / 2) * (1 / d));
}

const n = 7;

const firstTerm = 3;

const commonDifference = 2;

const sum = 
    sumOfFirstNTermsHP(n, firstTerm, commonDifference);
console.log(
    "Sum of first", n, "terms of harmonic progression:", sum);

Sum of first 7 terms of harmonic progression: 12.833333333333334

Time Complexity : O(1) , constant time

Space Complexity : O(1) , constant space