Sum of series 1*1*2! + 2*2*3! + ……..+ n*n*(n+1)!
Last Updated :
08 Sep, 2022
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++
#include <bits/stdc++.h>
using namespace std;
int factorial( int n)
{
int res = 1;
for ( int i = 2; i <= n; i++)
res = res * i;
return res;
}
int calculateSeries( int n)
{
return 2 + (n * n + n - 2) * factorial(n + 1);
}
int main()
{
int n = 3;
cout << calculateSeries(n);
return 0;
}
|
Java
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;
}
static int calculateSeries( int n)
{
return 2 + (n * n + n - 2 )
* factorial(n + 1 );
}
public static void main (String[] args)
{
int n = 3 ;
System.out.println(calculateSeries(n));
}
}
|
Python3
import math
def factorial(n):
res = 1
i = 2
for i in (n + 1 ):
res = res * i
return res
def calculateSeries(n):
return ( 2 + (n * n + n - 2 )
* math.factorial(n + 1 ))
n = 3
print (calculateSeries(n))
|
C#
using System;
class GFG {
static int factorial( int n)
{
int res = 1;
for ( int i = 2; i <= n; i++)
res = res * i;
return res;
}
static int calculateSeries( int n)
{
return 2 + (n * n + n - 2)
* factorial(n + 1);
}
public static void Main ()
{
int n = 3;
Console.WriteLine(calculateSeries(n));
}
}
|
PHP
<?php
function factorial( $n )
{
$res = 1;
for ( $i = 2; $i <= $n ; $i ++)
$res = $res * $i ;
return $res ;
}
function calculateSeries( $n )
{
return 2 + ( $n * $n + $n - 2) *
factorial( $n + 1);
}
$n = 3;
echo calculateSeries( $n );
?>
|
Javascript
<script>
function factorial( n)
{
let res = 1;
for (let i = 2; i <= n; i++)
res = res * i;
return res;
}
function calculateSeries( n)
{
return 2 + (n * n + n - 2)
* factorial(n + 1);
}
let n = 3;
document.write(calculateSeries(n));
</script>
|
Time Complexity : O(n)
Auxiliary Space: O(1)
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