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

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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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. 
?> 

Output:

Time Complexity: O(n²)

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. 
?> 

Output:

Time Complexity: O(n)

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. 
?> 

Output :

Time Complexity: O(1)

Please refer sum of squares of natural numbers for details of above formula and more optiimizations.

My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

PHP

C++

Java

Python3

C#

PHP

C++

Java

Python3

C#

PHP

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