# 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 ` `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

 ` `

Output:

`385`

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 ` `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

 ` `

Output:

`385`

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 ` `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

 ` `

Output :

`385`

Time Complexity: O(1)

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

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