In the previous article, we have discussed about Java Program to Find the Sum of Series 1^2/a + 3^2/a^2 + 5^2/a^3 + …… + N
In this article we are going to see how to find sum of the series 1/x + 1/x^2 + 1/x^3 + …… + 1/x^n by using Java programming language.
Java Program to Find the Sum of Series 1/x + 1/x^2 + 1/x^3 + …… + 1/x^n
On observing the pattern carefully, we can see Numerator is 1 (fixed)
In Denominator, the power/exponent of x is increasing by 1
Example:
x = 2 n = 3 1/2 + 1/2^2 + 1/2^3 = 1/2 + 1/4 + 1/8 = 0.5 + 0.25 + 0.125 = 0.875
Let’s see different ways to find sum of the series 1/x + 1/x^2 + 1/x^3 + …… + 1/x^n.
Method-1: Java Program to Find the Sum of Series 1/x + 1/x^2 + 1/x^3 + …… + 1/x^n By Using For Loop
Approach:
- Declare an integer variable say ‘
x
’ which holds the value of “x”. - Declare an integer variable say ‘
n
’ which holds the nth term of the series “n”. - Create Scanner class object.
- Prompt the user to enter value of
x
andn
. - Use a for loop
from i=1 to i<=n
- Inside loop we will first find the value of
1/Math.pow(x,i)
and then we will add the value in sum in every iteration. - Print the result.
Program:
import java.util.*; public class Main { public static void main(String args[]) { //creating object of Scanner class Scanner s = new Scanner(System.in); //Taking input of number of elements in the series System.out.println("Enter the value of x "); int x = s.nextInt(); //Taking input of number of elements in the series System.out.println("Enter the value of nth term 'n' "); int n = s.nextInt(); //for loop to print the series double sum = 0; for (int i = 1; i <= n; i++) sum += 1 / Math.pow(x, i); System.out.println("Sum of the series is " + sum); } }
Output: Enter the value of x 2 Enter the value of nth term 'n' 3 Sum of the series is 0.875
Method-2: Java Program to Find the Sum of Series 1/x + 1/x^2 + 1/x^3 + …… + 1/x^n By Using While Loop
Approach:
- Declare an integer variable say ‘
x
’ which holds the value of “x”. - Declare an integer variable say ‘
n
’ which holds the nth term of the series “n”. - Create Scanner class object.
- Prompt the user to enter value of
x
andn
. - Use a while loop
from i=1 to i<=n
- Inside loop we will first find the value of
1/Math.pow(x,i)
and then we will add the value in sum in every iteration. - Print the result.
Program:
import java.util.*; public class Main { public static void main(String args[]) { //creating object of Scanner class Scanner s = new Scanner(System.in); //Taking input of number of elements in the series System.out.println("Enter the value of x "); int x = s.nextInt(); //Taking input of number of elements in the series System.out.println("Enter the value of nth term 'n' "); int n = s.nextInt(); //while loop to print the series double sum = 0; int i = 1; while(i <= n) { sum += 1 / Math.pow(x, i); i ++; } System.out.println("sum of the series is " + sum); } }
Output: Enter the value of x 2 Enter the value of nth term 'n' 3 sum of the series is 0.875
Method-3: Java Program to Find the Sum of Series 1/x + 1/x^2 + 1/x^3 + …… + 1/x^n By Using User Defined Method
Approach:
- Declare an integer variable say ‘
x
’ which holds the value of “x”. - Declare an integer variable say ‘
n
’ which holds the nth term of the series “n”. - Create Scanner class object.
- Prompt the user to enter value of
x
andn
. - Call a method
m1()
by passingx
andn
as parameter. - Inside method use a for loop
from i=1 to i<=n
- Inside loop we will first find the value of
1/Math.pow(x,i)
and then we will add the value in sum in every iteration. - Print the result.
Program:
import java.util.*; public class Main { public static void main(String[] args) { // creating object of scanner class Scanner s = new Scanner(System.in); //Taking input of number of elements in the series System.out.println("Enter the value of x "); int x = s.nextInt(); //Taking input of number of elements in the series System.out.println("Enter the value of nth term 'n' "); int n = s.nextInt(); // calling m1 method to print the series m1(x,n); } public static void m1(int x, int n) { //for loop to print the series double sum = 0; for (int i = 1; i <= n; i++) sum += 1 / Math.pow(x, i); System.out.println("Sum of the series is " + sum); } }
Output: Enter the value of x 5 Enter the value of nth term 'n' 10 Sum of the series is 0.24999997440000005
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