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; ` `} ` |

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## 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)); ` ` ` `} ` `} ` |

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## 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. ` |

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## 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... ` |

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## 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. ` `?> ` |

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**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 so1

^{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)

= 16FROM THIS WE HAVE NOTICE THAT 1, 4, 9 GET CANCELLED FROM THE SERIES

ONLY 16 IS LEFT WHICH IS EQUAL TO THE SQUARE OF NSo 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; ` `} ` |

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## 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)); ` ` ` `} ` `} ` |

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## 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. ` |

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## 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. ` |

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## 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. ` `?> ` |

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**Output:**

The sum of n term is: 10000

Time complexity – O(1)

Space complexity – O(1)

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