# Sum of the series 1 + (1+3) + (1+3+5) + (1+3+5+7) + …… + (1+3+5+7+…+(2n-1))

Given a positive integer n. The problem is to find the sum of the given series 1 + (1+2) + (1+2+3) + (1+2+3+4) + …… + (1+2+3+4+…+n), where i-th term in the series is the sum of first i odd natural numbers.

Examples:

```Input : n = 2
Output : 5
(1) + (1+3) = 5```
```Input : n = 5
Output : 55
(1) + (1+3) + (1+3+5) + (1+3+5+7) + (1+3+5+7+9) = 55 ```
Recommended Practice

Naive Approach: Using two loops get the sum of each i-th term and then add those sum to the final sum.

## C++

 `// C++ implementation to find the ` `// sum of the given series` `#include `   `using` `namespace` `std;`   `// function to find the ` `// sum of the given series` `int` `sumOfTheSeries(``int` `n)` `{` `    ``int` `sum = 0;` `    ``for` `(``int` `i = 1; i <= n; i++) {`   `        ``// first term of each i-th term` `        ``int` `k = 1;` `        ``for` `(``int` `j = 1; j <= i; j++) {` `            ``sum += k;`   `            ``// next term` `            ``k += 2;` `        ``}` `    ``}`   `    ``// required sum` `    ``return` `sum;` `}`   `// Driver program ` `int` `main()` `{` `    ``int` `n = 5;` `    ``cout << ``"Sum = "` `         ``<< sumOfTheSeries(n);` `    ``return` `0;` `}`

## Java

 `// Java implementation to find ` `// the sum of the given series` `import` `java.util.*;`   `class` `GFG {` `    `  `    ``// function to find the sum` `    ``// of the given series` `    ``static` `int` `sumOfTheSeries(``int` `n)` `    ``{` `        ``int` `sum = ``0``;` `        ``for` `(``int` `i = ``1``; i <= n; i++)` `        ``{` `     `  `            ``// first term of each ` `            ``// i-th term` `            ``int` `k = ``1``;` `            ``for` `(``int` `j = ``1``; j <= i; j++)` `            ``{` `                ``sum += k;` `     `  `                ``// next term` `                ``k += ``2``;` `            ``}` `        ``}` `     `  `        ``// required sum` `        ``return` `sum;` `    ``}`   `    ``/* Driver program */` `    ``public` `static` `void` `main(String[] args) ` `    ``{` `         ``int` `n = ``5``;` `         ``System.out.println(``"Sum = "` `+ ` `                        ``sumOfTheSeries(n));` `    ``}` `}`   `// This code is contributed by Arnav Kr. Mandal.`

## Python3

 `# Python3 implementation to find` `# the sum of the given series`   `# function to find the sum` `# of the given series`     `def` `sumOfTheSeries(n):` `    ``sum` `=` `0` `    ``for` `i ``in` `range``(``1``, n ``+` `1``):`   `        ``# first term of each i-th term` `        ``k ``=` `1` `        ``for` `j ``in` `range``(``1``, i``+``1``):` `            ``sum` `+``=` `k`   `            ``# next term` `            ``k ``+``=` `2`   `    ``# required sum` `    ``return` `sum`     `# Driver program` `n ``=` `5` `print``(``"Sum ="``, sumOfTheSeries(n))`   `# This code is contributed by "Sharad_Bhardwaj".`

## C#

 `// C# implementation to find` `// the sum of the given series` `using` `System;`   `class` `GFG {`   `    ``// function to find the sum` `    ``// of the given series` `    ``static` `int` `sumOfTheSeries(``int` `n)` `    ``{` `        ``int` `sum = 0;` `        ``for` `(``int` `i = 1; i <= n; i++) {`   `            ``// first term of each` `            ``// i-th term` `            ``int` `k = 1;` `            ``for` `(``int` `j = 1; j <= i; j++) {` `                ``sum += k;`   `                ``// next term` `                ``k += 2;` `            ``}` `        ``}`   `        ``// required sum` `        ``return` `sum;` `    ``}`   `    ``/* Driver program */` `    ``public` `static` `void` `Main()` `    ``{` `        ``int` `n = 5;` `        ``Console.Write(``"Sum = "` `+ ` `                     ``sumOfTheSeries(n));` `    ``}` `}`   `// This code is contributed by vt_m.`

## php

 ``

## Javascript

 ``

Output:

`Sum = 55`

Time complexity: O(n2)

Auxiliary space: O(1)

Efficient Approach:

Let an be the n-th term of the given series.

```an = (1 + 3 + 5 + 7 + (2n-1))
= sum of first n odd numbers
= n2```

Refer this post for proof of the above formula. Now,

Refer this post for proof of the above formula.

## C++

 `// C++ implementation to find the sum` `// of the given series` `#include ` `using` `namespace` `std;`   `// function to find the sum` `// of the given series` `int` `sumOfTheSeries(``int` `n)` `{` `    ``// required sum` `    ``return` `(n * (n + 1) / 2) * (2 * n + 1) / 3;` `}`   `// Driver program to test above` `int` `main()` `{` `    ``int` `n = 5;` `    ``cout << ``"Sum = "` `<< sumOfTheSeries(n);` `    ``return` `0;` `}`

## Java

 `// Java implementation to find ` `// the sum of the given series` `import` `java.io.*;`   `class` `GfG {` `    `  `// function to find the sum` `// of the given series` `static` `int` `sumOfTheSeries(``int` `n)` `{` `    ``// required sum` `    ``return` `(n * (n + ``1``) / ``2``) *` `            ``(``2` `* n + ``1``) / ``3``;` `}` `    `    `// Driver program to test above` `public` `static` `void` `main (String[] args) ` `{` `    ``int` `n = ``5``;` `    `  `    ``System.out.println(``"Sum = "``+ ` `                ``sumOfTheSeries(n));`   `}`   `}`   `// This code is contributed by Gitanjali.`

## Python3

 `# Python3 implementation to find` `# the sum of the given series`   `# function to find the sum` `# of the given series` `def` `sumOfTheSeries( n ):` `    `  `    ``# required sum` `    ``return` `int``((n ``*` `(n ``+` `1``) ``/` `2``) ``*` `            ``(``2` `*` `n ``+` `1``) ``/` `3``)` `            `  `# Driver program to test above` `n ``=` `5` `print``(``"Sum ="``, sumOfTheSeries(n))`   `# This code is contributed by "Sharad_Bhardwaj".`

## C#

 `// C# implementation to find` `// the sum of the given series` `using` `System;`   `class` `GfG {`   `    ``// function to find the sum` `    ``// of the given series` `    ``static` `int` `sumOfTheSeries(``int` `n)` `    ``{` `        ``// required sum` `        ``return` `(n * (n + 1) / 2) * ` `                      ``(2 * n + 1) / 3;` `    ``}`   `    ``// Driver program to test above` `    ``public` `static` `void` `Main()` `    ``{` `        ``int` `n = 5;`   `        ``Console.Write(``"Sum = "` `+ ` `                   ``sumOfTheSeries(n));` `    ``}` `}`   `// This code is contributed by vt_m.`

## PHP

 ``

## Javascript

 ``

Output:

`Sum = 55`

Time complexity: O(1)

Auxiliary space: O(1)

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