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

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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