# 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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