# 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 ``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

 ``

## Javascript

 ``

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 ``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

 ``

## Javascript

 ``

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 ``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

 ``

## Javascript

 ``

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.

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