JavaScript Program for Sum of Infinite Terms in Geometric Progression
Geometric Progression is a sequence of numbers whose next term is calculated by multiplying the current term with a fixed number known as the common ratio.
Below are the approaches to find the sum of infinite terms in a Geometric progression using JavaScript:
Table of Content
- Using Iterative Approach
- Using Recursive Approach
- Using Direct Formula
Using Iterative Approach
In this approach, we use the while loop to iterate continuously and add terms to the sum until convergence. In each iteration, we will add the current term to the sum and update the value of nTerm by multiplying it with the common ratio r.
Example: The below code uses the iterative approach to calculate the sum of infinite terms in GP.
function sumOfInfiniteTermsGPIterative(a, r) {
if (Math.abs(r) >= 1) {
return "Sum does not converge (|r| >= 1)";
}
let sum = 0;
let nterm = a;
let iteration = 1500;
while (iteration > 0) {
sum += nterm;
nterm *= r;
iteration--;
}
return sum;
}
console.log(sumOfInfiniteTermsGPIterative(10, 0.8));
console.log(sumOfInfiniteTermsGPIterative(8, 0.5));
Output
50 16
Time Complexity : O(1), as the loop iterates constant 1500 times.
Space Complexity : O(1), constant space.
Using Recursive Approach
In this approach, we will define a recursive function. This function stops when the absolute value of the current term becomes very small, indicating convergence. Else, we will recursively call the function and calculate the sum of the current term and the sum of subsequent terms by multiplying the current term by the common ratio r and adding it to the sum of subsequent terms.
Example: The below code uses recursive function to calculate the sum of a infinite GP series.
function sumOfInfiniteTermsGPRecursive(a, r) {
if (Math.abs(r) >= 1) {
return "Sum does not converge (|r| >= 1)";
}
function recursive(nterm) {
if (Math.abs(nterm) < 0.0001) {
return 0;
}
return nterm + recursive(nterm * r);
}
return recursive(a);
}
console.log(sumOfInfiniteTermsGPRecursive(10, 0.8));
console.log(sumOfInfiniteTermsGPRecursive(8, 0.5));
Output
49.999543280738344 15.9998779296875
Time Complexity: O(log n)
Space Complexity: O(log n)
Using Direct Formula
The sum of the infinite terms of a Geometric Progression series can also be calculated using the direct mathematical formula.
Syntax:
S ∞ = a/ (1-r) where ∣r∣ < 1
where, S∞ is the sum of infinite terms of G.P., a is the first term of G.P., r is the common ratio of G.P. (for calculating sum of infinite terms in G.P. the absolute value of the common ratio must be less than 1)
Example: The below code will explain the use of the mathematical formula to calculate the sum of the infinite terms of GP.
function sumOfInfiniteTermsGPFormula(a, r) {
if (Math.abs(r) >= 1) {
return "Sum of infinite terms does not exist (diverges)";
}
return a / (1 - r);
}
console.log(sumOfInfiniteTermsGPFormula(10, 0.8));
console.log(sumOfInfiniteTermsGPFormula(8, 0.5));
Output
50.000000000000014 16
Time Complexity : O(1), constant time
Space Complexity : O(1), constant space