Find Sum of the Series 0.6, 0.06, 0.006, 0.0006, …to n Terms in Java

8 May 2025 | 5 min read

Given the number of terms n, find the sum of the series 0.6, 0.06, 0.006, 0.0006,… up to n terms.

Input: n=4

Output: 0.6666

Explanation: Sum of the series up to 4 terms:

0.6+0.06+0.006+0.0006= 0.66660

Input: n=5

Output: 0.66666

Explanation: Sum of the series up to 5 terms:

0.6+0.06+0.006+0.0006+0.00006=0.66666

Approach: Using the Geometric Progression Formula

The Java program calculates the sum of a series where each term is 1/10 of the previous term, starting with 0.6. The sum is computed using the formula:

S_n = a * (1 - rⁿ) / (1 - r)

Here:

a = 0.6 (first term),
r = 0.1 (factor by which each term decreases),
n = 3 (number of terms).

Algorithm

Step 1: Assign a = 0.6 (first term), r = 0.1 (common ratio), and n = 3 (number of terms).

Step 2: Use Math.pow(r, n) to compute rⁿ.

Step 3: Apply the formula S_n = a * (1 - Math.pow(r, n)) / (1 - r) to calculate the sum of the series.

Step 4: Insert the values of a, r, and n into the formula to find the sum.

Step 5: Print the sum along with the values of a, r, and n, formatted to six decimal places.

Implementation

Output:

 
Sum of the series with a=0.60, r=0.10, n=3 = 0.666000

Approach: Using a Loop to Calculate the Sum

The approach uses a loop to iteratively calculate the sum of the series. In each iteration, the current term is added to the sum, and the term is updated by multiplying it with the common ratio to calculate the next term.

Algorithm

Step 1: Set the values for n (number of terms), a (first term), and r (common ratio) in the series.

Step 2: Initialize sum = 0.0 and term = a (the first term).

Step 3: Use a for loop to iterate n times. In each iteration, add the current term to the sum and multiply the term by the common ratio r to compute the next term.

Step 4: Inside the loop, update the term by multiplying it by r.

Step 5: After the loop completes, output the sum of the series with 6 decimal places.

Implementation

File Name: SeriesSumCalculator.java

Output:

 
Sum of the series (using loop) = 0.666000

Approach: Using Recursion

The approach used in the code is a recursive method to calculate the sum of a geometric series. It repeatedly calls itself, reducing the number of terms (n) by one in each call, until it reaches the base case where only the first term is left.

Algorithm

Step 1: Define the values for the number of terms n, the initial term a, and the common ratio r in the sequence.

Step 2: Call the recursive function calculateSum(a, r, n) to determine the overall sum of the series.

Step 3: In the recursive function, verify if n equals 1. If accurate, yield the value of a, since only the initial term persists.

Step 4: If n > 1, return the addition of the current term a and make a recursive call to calculateSum(a * r, r, n - 1) to determine the sum of the following terms.

Step 5: After the recursion finishes, display the total of the series with a precision of 6 decimal points.

Implementation

File Name: SeriesSumCalculator,java

Output:

 
Sum of the series (using recursion) = 0.666000

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Find Sum of the Series 0.6, 0.06, 0.006, 0.0006, …to n Terms in Java

Approach: Using the Geometric Progression Formula

Algorithm

Implementation

Approach: Using a Loop to Calculate the Sum

Algorithm

Implementation

Approach: Using Recursion

Algorithm

Implementation

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