We are going to learn how we can find the sum of series: 1/1 + 1/2 + 1/3 + ...... till n terms using JavaScript.
Below are approaches to calculate sum of the series:
Table of Content
Using for loop
We will create a function and Initialize a variable named sum (set it 0 initially) to store the sum of the series. Use a for loop to iterate from 1 to n and in each iteration, add 1 / i to the sum. After the loop finishes, return the calculated sum.
Example: To demonstrate calculation of sum of given series using for loop.
// using for loop
function seriesSumForLoop(n) {
let sum = 0;
for (let i = 1; i <= n; i++) {
sum += 1 / i;
}
return sum;
}
// Number of terms
const n = 7;
const result = seriesSumForLoop(n);
console.log(`Sum of the series using
for loop is :`, result);
Output
Sum of the series using for loop is : 2.5928571428571425
Time complexity: O(n)
Space complexity: O(1)
Using Recursion
We will create a recursive function. The base case for this recursive function is, if value of n is 1 then it returns 1 , else in the recursive case, it calculates 1/n and adds it to the sum of the series for n-1 terms, which is obtained by recursively calling the function. The recursion continues until the base case is reached.
Example: To demonstrate calculation of given series using recursion.
// using recursion
function seriesSumRecursion(n) {
// Base case
if (n === 1) {
return 1;
}
// Recursive case
return 1 / n + seriesSumRecursion(n - 1);
}
// Number of terms
const n = 7;
const result = seriesSumRecursion(n);
console.log(`Sum of the series using
recursion is :`, result);
Output
Sum of the series using recursion is : 2.5928571428571425
Time complexity: O(n)
Space complexity: O(n)