In the previous article, we have discussed about Java Program to Find the Sum of Series 1 + (3/2!) + (5/3!) + (7/4!) + …… + N

In this article we are going to see how to print the sum of series 1 + 1/(1+2) + 1/(1+2+3) + … + 1/(1+2+3+…+n) by using Java programming language.

## Java Program to Find the Sum of Series 1 + 1 / (1+2) + 1 / (1+2+3) + … + 1 / (1+2+3+ … + N)

On observing the pattern carefully, we can see it is in the format of `a/b`

Numerator = 1 (fixed) in each term.

Denominator = Sum of `n`

term means

in first term sum of 1

in second term sum of 1+2

in third term sum of 1+2+3

in nth term sum of 1+2+3+…+n

So the series for n terms looks like 1 + 1 / (1+2) + 1 / (1+2+3) + ……… + 1 / (1+2+3+ … + N).

**Example:**

Suppose n = 3 Then series: 1 + (1/1+2) + (1/1+2+3) = 1 + 1/3 + 1/6 = 1 + 0.34 + 0.17 = 1.51

### Method-1: Java Program to Find the Sum of Series 1 + 1 / (1+2) + 1 / (1+2+3) + … + 1 / (1+2+3+ … + N) By Using For Loop

**Approach:**

- Declare an integer variable say ‘
`n`

’ which holds the value of Nth term. - Create Scanner class object.
- Prompt the user to enter a number as value of n.
- Declare an double variable say ‘
`sum`

‘ and initialize it to 0. - Use a for loop from
`i=1 to i<=n`

(incremented by 1) - Declare an long variable say ‘
`term`

‘ and initialize it to 0. - Inside for loop, we will again do a for loop from
`j =1 to j<=i`

(incremented by 1) - Inside this loop we will get the sum of n term and store it in the variable “
`term`

”. - Now in the loop we will find the value of
`1.0/ term`

and after that we will add it into`sum`

for 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 'n' "); int n = s.nextInt(); //for loop to print the series double sum = 0; for (int i = 1; i <= n; i++) { long term = 0; for (int j = 1; j <= i; j++) { term += j; } sum += (1.0 / term); } System.out.println("Sum of the series is " + sum); } }

Output: Enter the value of 'n' 3 Sum of the series is 1.5

### Method-1: Java Program to Find the Sum of Series 1 + 1 / (1+2) + 1 / (1+2+3) + … + 1 / (1+2+3+ … + N) By Using While Loop

**Approach:**

- Declare an integer variable say ‘
`n`

’ which holds the value of Nth term. - Create Scanner class object.
- Prompt the user to enter a number as value of n.
- Declare an double variable say ‘
`sum`

‘ and initialize it to 0. - Continue a While loop till
`i<=n`

(from i=1 and loop incremented by 1) - Declare an long variable say ‘
`term`

‘ and initialize it to 0. - Inside while loop, we will again do a while loop till
`j<=i`

(from j=1 and loop incremented by 1) - Inside this loop we will get the sum of n term and store it in the variable “
`term`

”. - Now in the loop we will find the value of
`1.0/ term`

and after that we will add it into`sum`

for 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 'n' "); int n = s.nextInt(); // while loop to print the series double sum = 0; int i = 1; while(i <= n) { long term = 0; int j = 1; while ( j <= i) { term += j; j++; } sum += (1.0 / term); i++; } System.out.println("Sum of the series is " + sum); } }

Output: Enter the value of 'n' 3 Sum of the series is 1.5

### Method-3: Java Program to Find the Sum of Series 1 + 1 / (1+2) + 1 / (1+2+3) + … + 1 / (1+2+3+ … + N) By Using User Defined Loop

**Approach:**

- Declare an integer variable say ‘
`n`

’ which holds the value of Nth term. - Create Scanner class object.
- Prompt the user to enter a number as value of n.
- Then call a user defined method say
`printSeries()`

by passing n as parameter. - Declare an double variable say ‘
`sum`

‘ and initialize it to 0. - Use a for loop from
`i=1 to i<=n`

(incremented by 1) - Declare an long variable say ‘
`term`

‘ and initialize it to 0. - Inside for loop, we will again do a for loop from
`j =1 to j<=i`

(incremented by 1) - Inside this loop we will get the sum of n term and store it in the variable “
`term`

”. - Now in the loop we will find the value of
`1.0/ term`

and after that we will add it into`sum`

for 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 'n' "); int n = s.nextInt(); // calling printSeries() method to print the series printSeries(n); } public static void printSeries(int n) { double sum=0; for (int i = 1; i <= n; i++) { long term = 0; for (int j = 1; j <= i; j++) { term += j; } sum += (1.0 / term); } System.out.println("Sum of the series is " + sum); } }

Output: Enter the value of 'n' 4 Sum of the series is 1.6

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