Given the value of the n. You have to find the sum of the series where the n^{th} term of the sequence is given by:

T_{n} = n^{2} – ( n – 1 )^{2}**Examples :**

Input : 3 Output : 9 Explanation: So here the tern of the sequence upto n = 3 are: 1, 3, 5 And hence the required sum is = 1 + 3 + 5 = 9 Input : 6 Output : 36

**Simple Approach**

Just use a loop and calculate the sum of each term and print the sum.

## C++

`// CPP program to find summation of series` `#include <bits/stdc++.h>` `using` `namespace` `std;` `int` `summingSeries(` `long` `n)` `{` ` ` `// use of loop to calculate` ` ` `// sum of each term` ` ` `int` `S = 0;` ` ` `for` `(` `int` `i = 1; i <= n; i++)` ` ` `S += i * i - (i - 1) * (i - 1);` ` ` ` ` `return` `S;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `n = 100;` ` ` `cout << ` `"The sum of n term is: "` ` ` `<< summingSeries(n) << endl;` ` ` `return` `0;` `}` |

## Java

`// JAVA program to find summation of series` `import` `java.io.*;` `import` `java.math.*;` `import` `java.text.*;` `import` `java.util.*;` `import` `java.util.regex.*;` `class` `GFG` `{` ` ` `// function to calulate sum of series` ` ` `static` `int` `summingSeries(` `long` `n)` ` ` `{` ` ` `// use of loop to calculate` ` ` `// sum of each term` ` ` `int` `S = ` `0` `;` ` ` `for` `(i = ` `1` `; i <= n; i++)` ` ` `S += i * i - (i - ` `1` `) * (i - ` `1` `); ` ` ` ` ` `return` `S;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `int` `n = ` `100` `;` ` ` `System.out.println(` `"The sum of n term is: "` `+` ` ` `summingSeries(n));` ` ` `}` `}` |

## Python3

`# Python3 program to find summation` `# of series` `def` `summingSeries(n):` ` ` `# use of loop to calculate` ` ` `# sum of each term` ` ` `S ` `=` `0` ` ` `for` `i ` `in` `range` `(` `1` `, n` `+` `1` `):` ` ` `S ` `+` `=` `i ` `*` `i ` `-` `(i ` `-` `1` `) ` `*` `(i ` `-` `1` `)` ` ` ` ` `return` `S` `# Driver Code` `n ` `=` `100` `print` `(` `"The sum of n term is: "` `,` ` ` `summingSeries(n), sep ` `=` `"")` `# This code is contributed by Smitha.` |

## C#

`// C# program to illustrate...` `// Summation of series` `using` `System;` `class` `GFG` `{` ` ` `// function to calculate sum of series` ` ` `static` `int` `summingSeries(` `long` `n)` ` ` `{` ` ` `// Using the pow function calculate` ` ` `// the sum of the series` ` ` `return` `(` `int` `)Math.Pow(n, 2);` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `Main(String[] args)` ` ` `{` ` ` `int` `n = 100;` ` ` `Console.Write(` `"The sum of n term is: "` `+` ` ` `summingSeries(n));` ` ` `}` `}` `// This code contribute by Parashar...` |

## PHP

`<?php` `// PHP program to find` `// summation of series` `function` `summingSeries( ` `$n` `)` `{` ` ` ` ` `// use of loop to calculate` ` ` `// sum of each term` ` ` `$S` `= 0;` ` ` `for` `(` `$i` `= 1; ` `$i` `<= ` `$n` `; ` `$i` `++)` ` ` `$S` `+= ` `$i` `* ` `$i` `- (` `$i` `- 1) *` ` ` `(` `$i` `- 1);` ` ` ` ` `return` `$S` `;` `}` `// Driver Code` `$n` `= 100;` `echo` `"The sum of n term is: "` `,` `summingSeries(` `$n` `) ;` `// This code contribute by vt_m.` `?>` |

## Javascript

`<script>` `// Javascript program to find summation of series` `function` `summingSeries(n)` `{` ` ` `// use of loop to calculate` ` ` `// sum of each term` ` ` `let S = 0;` ` ` `for` `(let i = 1; i <= n; i++)` ` ` `S += i * i - (i - 1) * (i - 1);` ` ` ` ` `return` `S;` `}` `// Driver Code` `let n = 100;` `document.write(` `"The sum of n term is: "` `+ summingSeries(n));` `// This code is contributed by rishavmahato348.` `</script>` |

**Output:**

The sum of n term is: 10000

**Time complexity –** O(N) **Space complexity –** O(1)**Efficient Approach**

Use of mathematical approach can solve this problem in more efficient way.

T

_{n}= n^{2}– (n-1)^{2}

Sum of the series is given by (S) = SUM( T_{n})

LET US TAKE A EXAMPLE IF

N = 4

It means there should be 4 terms in the series so

1^{st}term = 1^{2}– ( 1 – 1 )^{2}

2^{nd}term = 2^{2}– ( 2 – 1 )^{2}

3^{th}term = 3^{2}– ( 3 – 1 )^{2}

4^{th}term = 4^{2}– ( 3 – 1 )^{2}SO SUM IS GIVEN BY= (1 – 0) + (4 – 1) + (9 – 4) + (16 – 9)

= 16

FROM THIS WE HAVE NOTICE THAT 1, 4, 9 GET CANCELLED FROM THE SERIES

ONLY 16 IS LEFT WHICH IS EQUAL TO THE SQUARE OF N

So from the above series we notice that each term gets canceled from the next term, only the last term is left which is equal to N^{2}.

## C++

`// CPP program to illustrate...` `// Summation of series` `#include <bits/stdc++.h>` `using` `namespace` `std;` `int` `summingSeries(` `long` `n)` `{` ` ` `// Sum of n terms is n^2` ` ` `return` `pow` `(n, 2);` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `n = 100;` ` ` `cout << ` `"The sum of n term is: "` ` ` `<< summingSeries(n) << endl;` ` ` `return` `0;` `}` |

## Java

`// JAVA program to illustrate...` `// Summation of series` `import` `java.io.*;` `import` `java.math.*;` `import` `java.text.*;` `import` `java.util.*;` `import` `java.util.regex.*;` `class` `GFG` `{` ` ` `// function to calculate sum of series` ` ` `static` `int` `summingSeries(` `long` `n)` ` ` `{` ` ` `// Using the pow function calculate` ` ` `// the sum of the series` ` ` `return` `(` `int` `)Math.pow(n, ` `2` `);` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `int` `n = ` `100` `;` ` ` `System.out.println(` `"The sum of n term is: "` `+` ` ` `summingSeries(n));` ` ` `}` `}` |

## Python3

`# Python3 program to illustrate...` `# Summation of series` `import` `math` `def` `summingSeries(n):` ` ` `# Sum of n terms is n^2` ` ` `return` `math.` `pow` `(n, ` `2` `)` `# Driver Code` `n ` `=` `100` `print` `(` `"The sum of n term is: "` `,` ` ` `summingSeries(n))` `# This code is contributed by mits.` |

## C#

`// C# program to illustrate...` `// Summation of series` `using` `System;` `class` `GFG` `{` ` ` `// function to calculate sum of series` ` ` `static` `int` `summingSeries(` `long` `n)` ` ` `{` ` ` `// Using the pow function calculate` ` ` `// the sum of the series` ` ` `return` `(` `int` `)Math.Pow(n, 2);` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `n = 100;` ` ` `Console.Write(` `"The sum of n term is: "` `+` ` ` `summingSeries(n));` ` ` `}` `}` `// This code is contributed by nitin mittal.` |

## PHP

`<?php` `// PHP program to illustrate...` `// Summation of series` `function` `summingSeries(` `$n` `)` `{` ` ` `// Sum of n terms is n^2` ` ` `return` `pow(` `$n` `, 2);` `}` `// Driver Code` `$n` `= 100;` `echo` `"The sum of n term is: "` `,` `summingSeries(` `$n` `);` `// This code contribute by vt_m.` `?>` |

## Javascript

`<script>` `// Javascript program to illustrate...` `// Summation of series` `function` `summingSeries(n)` `{` ` ` `// Sum of n terms is n^2` ` ` `return` `Math.pow(n, 2);` `}` `// Driver Code` `let n = 100;` `document.write(` `"The sum of n term is: "` ` ` `+ summingSeries(n) + ` `"<br>"` `);` ` ` ` ` `// This code is contributed by subham348.` `</script>` |

**Output:**

The sum of n term is: 10000

**Time complexity – O(1) ****Space complexity – O(1) **

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