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

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: 

385

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: 

385

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 : 

385

Time Complexity: O(1)

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