Program to find sum of series 1 + 2 + 2 + 3 + 3 + 3 + . . . + n

0 0 7 minutes read

Given a positive integer n and the task is to find sum of series 1 + 2 + 2 + 3 + 3 + 3 + . . . + n.
Examples:

Input : n = 5
Output : 55
   = 1 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 
     4 + 5 + 5 + 5 + 5 + 5.
   = 55

Input : n = 10
Output : 385

Addition method: In addition method sum all the elements one by one.
Below is the implementation of this approach.

C++

// Program to find
// sum of series
// 1 + 2 + 2 + 3 + 
// . . . + n
#include <bits/stdc++.h>
using namespace std;
 
// Function that find
// sum of series.
int sumOfSeries(int n)
{
    int sum = 0;
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= i; j++)
            sum = sum + i;
    return sum;
}
 
// Driver function
int main()
{
    int n = 10;
 
    // Function call
    cout << sumOfSeries(n);
    return 0;
}

Java

// Java Program to
// find sum of 
// series
// 1 + 2 + 2 + 3 + 
// . . . + n
public class GfG{
 
    // Function that find 
    // sum of series.
    static int sumOfSeries(int n)
    {
        int sum = 0;
         
        for (int i = 1; i <= n; i++)
            for (int j = 1; j <= i; j++)
                sum = sum + i;
         
        return sum;
    }
     
    // Driver Code
    public static void main(String s[])
    {
        int n = 10;
        System.out.println(sumOfSeries(n));
         
    }
} 
 
// This code is contributed by Gitanjali

Python3

# Python3 Program to 
# find sum of series
# 1 + 2 + 2 + 3 + 
# . . . + n
import math 
 
# Function that find
# sum of series.
def sumOfSeries( n):
    sum = 0
    for i in range(1, n+1):
        sum = sum + i * i
    return sum
 
# Driver method
n = 10
 
# Function call
print (sumOfSeries(n))
 
# This code is contributed by Gitanjali 

C#

// C# Program to find sum of
// series 1 + 2 + 2 + 3 + . . . + n
using System;
 
public class GfG {
 
    // Function that find
    // sum of series.
    static int sumOfSeries(int n)
    {
        int sum = 0;
 
        for (int i = 1; i <= n; i++)
            for (int j = 1; j <= i; j++)
                sum = sum + i;
 
        return sum;
    }
 
    // Driver Code
    public static void Main()
    {
        int n = 10;
        Console.Write(sumOfSeries(n));
    }
}
 
// This code is contributed by vt_m.

PHP

<?php
// Program to find
// sum of series
// 1 + 2 + 2 + 3 + 
// . . . + n
 
// Function that find
// sum of series.
function sumOfSeries($n)
{
    $sum = 0;
    for ($i = 1; $i <= $n; $i++)
        for ($j = 1; $j <= $i; $j++)
            $sum = $sum + $i;
    return $sum;
}
 
// Driver Code
$n = 10;
 
// Function call
echo(sumOfSeries($n));
 
// This code is contributed by Ajit.
?>

Javascript

<script>
// Javascript Program to
// find sum of 
// series
// 1 + 2 + 2 + 3 + 
// . . . + n
 
    // Function that find
    // sum of series.
    function sumOfSeries( n) {
        let sum = 0;
 
        for (let i = 1; i <= n; i++)
            for (let j = 1; j <= i; j++)
                sum = sum + i;
 
        return sum;
    }
 
    // Driver Code
        let n = 10;
        document.write(sumOfSeries(n));
 
 
// This code contributed by Princi Singh
 
</script>

Output:

Time Complexity: O(n²)

Auxiliary Space: O(1)
Multiplication method:In multiplication method every elements multiply by itself and then add them.

   Input n = 10
   sum = 1 + 2 + 2 + 3 + 3 + 3 + 4 + . . . + 10
       = 1 + 2 * 2 + 3 * 3 + 4 * 4 + . . . + 10 * 10
       = 1 + 4 + 9 + 16 + . . . + 100
       = 385

C++

// Program to find
// sum of series
// 1 + 2 + 2 + 3 + 
// . . . + n
#include <bits/stdc++.h>
using namespace std;
 
// Function to find 
// sum of series.
int sumOfSeries(int n)
{
    int sum = 0;
    for (int i = 1; i <= n; i++)
        sum = sum + i * i;
    return sum;
}
 
// Driver function.
int main()
{
    int n = 10;
 
    // Function call
    cout << sumOfSeries(n);
    return 0;
}

Java

// Java Program to 
// find sum of series
// 1 + 2 + 2 + 3 + 
// . . . + n
public class GfG{
 
    // Function that find sum of series.
    static int sumOfSeries(int n)
    {
        int sum = 0;
        for (int i = 1; i <= n; i++)
            sum = sum + i * i;
        return sum;
    }
 
    // Driver Code 
    public static void main(String args[])
    {
        int n = 10;
        System.out.println(sumOfSeries(n));
         
    }
} 
 
// This code is contributed by Gitanjali

Python3

# Python3 Program to 
# find sum of series
# 1 + 2 + 2 + 3 + 
# . . . + n
import math 
 
# Function that find 
# sum of series.
def sumOfSeries( n):
    sum = 0
    for i in range(1, n+1):
        sum = sum + i * i
    return sum
 
# Driver method
n = 10
# Function call
print (sumOfSeries(n))
 
# This code is contributed by Gitanjali.

C#

// C# Program to find sum of series
// 1 + 2 + 2 + 3 + . . . + n
using System;
 
class GfG {
 
    // Function that find sum of series.
    static int sumOfSeries(int n)
    {
        int sum = 0;
        for (int i = 1; i <= n; i++)
            sum = sum + i * i;
        return sum;
    }
 
    // Driver Code 
    public static void Main()
    {
        int n = 10;
        Console.WriteLine(sumOfSeries(n));
         
    }
} 
 
// This code is contributed by anuj_67.

PHP

<?php
// Program to find
// sum of series
// 1 + 2 + 2 + 3 + 
// . . . + n
 
// Function to find 
// sum of series.
function sumOfSeries($n)
{
    $sum = 0;
    for ($i = 1; $i <= $n; $i++)
        $sum = $sum + $i * $i;
    return $sum;
}
 
// Driver Code
$n = 10;
 
// Function call
echo(sumOfSeries($n));
 
// This code is contributed by Ajit.
?>

Javascript

<script>
// javascript Program to 
// find sum of series
// 1 + 2 + 2 + 3 + 
// . . . + n
 
    // Function that find sum of series.
    function sumOfSeries(n)
    {
        var sum = 0;
        for (let i = 1; i <= n; i++)
            sum = sum + i * i;
        return sum;
    }
 
    // Driver Code
    var n = 10;
    document.write(sumOfSeries(n));
 
// This code is contributed by Amit Katiyar
</script>

Output:

Time Complexity: O(n)

Auxiliary Space: O(1)
Using formula: We also use formula to find the sum of series.

    Input n = 10;
   Sum of series = (n * (n + 1) * (2 * n + 1)) / 6
    put n = 10 in the above formula
    sum = (10 * (10 + 1) * (2 * 10 + 1)) / 6
        = (10 * 11 * 21) / 6
        = 385

C++

// C++ Program to
// find sum of series
// 1 + 2 + 2 + 3 + 
// . . . + n
#include <bits/stdc++.h>
using namespace std;
 
// Function to find 
// sum of series.
int sumOfSeries(int n)
{
    return (n * (n + 1) * (2 * n + 1)) / 6;
}
 
// Driver function
int main()
{
    int n = 10;
 
    // Function call
    cout << sumOfSeries(n);
    return 0;
}

Java

// Java Program to 
// find sum of series
// 1 + 2 + 2 + 3 + 
// . . . + n
public class GfG
{
    // Function that find
    // sum of series.
    static int sumOfSeries(int n)
    {
        return (n * (n + 1) * (2 * n + 1)) / 6;
    }
     
    // Driver Code
    public static void main(String s[])
    {
        int n = 10;
        System.out.println(sumOfSeries(n));
         
    }
} 
 
// This code is contributed by 'Gitanjali'.

Python3

# Python3 Program to
# find sum of series
# 1 + 2 + 2 + 3 + 
# . . . + n
import math 
 
# Function that find
# sum of series.
def sumOfSeries( n):
    return ((n * (n + 1) * (2 * n + 1)) / 6)
 
# Driver method
n = 10
 
# Function call
print (sumOfSeries(n))
 
# This code is contributed by Gitanjali

C#

// C# Program to find sum of series
// 1 + 2 + 2 + 3 + . . . + n
using System;
 
public class GfG {
     
    // Function that find
    // sum of series.
    static int sumOfSeries(int n)
    {
        return (n * (n + 1) * (2 * n + 1)) / 6;
    }
 
    // Driver Code
    public static void Main()
    {
        int n = 10;
        Console.WriteLine(sumOfSeries(n));
    }
}
 
// This code is contributed by 'vt_m'.

PHP

<?php
// PHP Program to
// find sum of series
// 1 + 2 + 2 + 3 + 
// . . . + n
 
// Function to find 
// sum of series.
function sumOfSeries($n)
{
    return ($n * ($n + 1) * 
           (2 * $n + 1)) / 6;
}
 
// Driver Code
$n = 10;
 
// Function call
echo(sumOfSeries($n));
 
// This code is contributed by Ajit.
?>

Javascript

<script>
// javascript Program to 
// find sum of series
// 1 + 2 + 2 + 3 + 
// . . . + n
 
// Function that find
// sum of series.
function sumOfSeries(n)
{
    return (n * (n + 1) * (2 * n + 1)) / 6;
}
 
// Driver Code
var n = 10;
document.write(sumOfSeries(n));
 
 
// This code is contributed by Amit Katiyar 
</script>

Output :

Time Complexity: O(1)

Auxiliary Space: O(1)
Please refer sum of squares of natural numbers for details of above formula and more optimizations.

Recommended

Solve DSA problems on GfG Practice.

Solve Problems

Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 zambiatek!