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Sum of series 1*1*2! + 2*2*3! + ……..+ n*n*(n+1)!
• Difficulty Level : Easy
• Last Updated : 27 Apr, 2021

Given n, we need to find sum of 1*1*2! + 2*2*3! + ……..+ n*n*(n+1)!
Examples:

Input: 1
Output: 2
Input: 3
Output: 242

We may assume that overflow does not happen.

A simple solution is to compute terms one by one and add to result.
An efficient solution is based on direct formula 2 + (n*n + n – 2) * (n + 1)!
The working of formula is based on this post.

## C++

 `// CPP program to find sum of the series.``#include ``using` `namespace` `std;` `int` `factorial(``int` `n)``{``    ``int` `res = 1;``    ``for` `(``int` `i = 2; i <= n; i++)``        ``res = res * i;``    ``return` `res;``}` `// Function to calculate required series``int` `calculateSeries(``int` `n)``{``    ``return` `2 + (n * n + n - 2) * factorial(n + 1);``}` `// Drivers code``int` `main()``{``    ``int` `n = 3;``    ``cout << calculateSeries(n);``    ``return` `0;``}`

## Java

 `// java program to find sum of the series.``import` `java.io.*;` `class` `GFG {``    ` `    ``static` `int` `factorial(``int` `n)``    ``{``        ``int` `res = ``1``;``        ``for` `(``int` `i = ``2``; i <= n; i++)``            ``res = res * i;``        ``return` `res;``    ``}``    ` `    ``// Function to calculate required series``    ``static` `int` `calculateSeries(``int` `n)``    ``{``        ``return` `2` `+ (n * n + n - ``2``)``                      ``* factorial(n + ``1``);``    ``}``    ` `    ``// Drivers code``    ``public` `static` `void` `main (String[] args)``    ``{``        ``int` `n = ``3``;``        ``System.out.println(calculateSeries(n));``    ``}``}` `// This code is contributed by anuj_67.`

## Python3

 `# Python program to find sum of``# the series.``import` `math` `def` `factorial(n):``    ``res ``=` `1``    ``i ``=` `2``    ``for` `i ``in` `(n``+``1``):``        ``res ``=` `res ``*` `i``    ``return` `res``    ` `# Function to calculate required``# series``def` `calculateSeries(n):``    ``return` `(``2` `+` `(n ``*` `n ``+` `n ``-` `2``)``        ``*` `math.factorial(n ``+` `1``))` `# Driver code``n ``=` `3``print``(calculateSeries(n))` `# This code is contributed by``# Prateek bajaj`

## C#

 `// C# program to find sum of the series.``using` `System;``class` `GFG {``    ` `    ``static` `int` `factorial(``int` `n)``    ``{``        ``int` `res = 1;``        ``for` `(``int` `i = 2; i <= n; i++)``            ``res = res * i;``        ``return` `res;``    ``}``    ` `    ``// Function to calculate required series``    ``static` `int` `calculateSeries(``int` `n)``    ``{``        ``return` `2 + (n * n + n - 2)``                 ``* factorial(n + 1);``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main ()``    ``{``        ``int` `n = 3;``        ``Console.WriteLine(calculateSeries(n));``    ``}``}` `// This code is contributed by anuj_67.`

## PHP

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## Javascript

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Output:
`242`

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