Given a number N. The task is to write a program to find the Nth term in the below series:
1, 4, 15, 72, 420…
Examples:
Input: 3
Output: 15
Explanation: For N = 3, we know that the factorial of 3 is 6 Nth term = 6*(3+2)/2Input: 6
Output: 2880
Explanation: For N = 6, we know that the factorial of 6 is 720 Nth term = 620*(6+2)/2 = 2880
The idea is to first find the factorial of the given number N, that is N!. Now the N-th term in the above series will be:
N-th term = N! * (N + 2)/2
Below is the implementation of the above approach:
// CPP program to find N-th term of the series: // 1, 4, 15, 72, 420… #include <iostream> using namespace std;
// Function to find factorial of N int factorial( int N)
{ int fact = 1;
for ( int i = 1; i <= N; i++)
fact = fact * i;
// return factorial of N
return fact;
} // calculate Nth term of series int nthTerm( int N)
{ return (factorial(N) * (N + 2) / 2);
} // Driver Function int main()
{ int N = 6;
cout << nthTerm(N);
return 0;
} |
// Java program to find N-th // term of the series: // 1, 4, 15, 72, 420 import java.util.*;
import java.lang.*;
import java.io.*;
class GFG
{ // Function to find factorial of N static int factorial( int N)
{ int fact = 1 ;
for ( int i = 1 ; i <= N; i++)
fact = fact * i;
// return factorial of N
return fact;
} // calculate Nth term of series static int nthTerm( int N)
{ return (factorial(N) * (N + 2 ) / 2 );
} // Driver Code public static void main(String args[])
{ int N = 6 ;
System.out.println(nthTerm(N));
} } // This code is contributed by Subhadeep |
# Python 3 program to find # N-th term of the series: # 1, 4, 15, 72, 420… # Function for finding # factorial of N def factorial(N) :
fact = 1
for i in range ( 1 , N + 1 ) :
fact = fact * i
# return factorial of N
return fact
# Function for calculating # Nth term of series def nthTerm(N) :
# return nth term
return (factorial(N) * (N + 2 ) / / 2 )
# Driver code if __name__ = = "__main__" :
N = 6
# Function Calling
print (nthTerm(N))
# This code is contributed # by ANKITRAI1 |
// C# program to find N-th // term of the series: // 1, 4, 15, 72, 420 using System;
class GFG
{ // Function to find factorial of N static int factorial( int N)
{ int fact = 1;
for ( int i = 1; i <= N; i++)
fact = fact * i;
// return factorial of N
return fact;
} // calculate Nth term of series static int nthTerm( int N)
{ return (factorial(N) * (N + 2) / 2);
} // Driver Code public static void Main()
{ int N = 6;
Console.Write(nthTerm(N));
} } // This code is contributed by ChitraNayal |
<?php // PHP program to find // N-th term of the series: // 1, 4, 15, 72, 420… // Function for finding // factorial of N function factorial( $N )
{ $fact = 1;
for ( $i = 1; $i <= $N ; $i ++)
$fact = $fact * $i ;
// return factorial of N
return $fact ;
} // Function for calculating // Nth term of series function nthTerm( $N )
{ // return nth term
return (factorial( $N ) *
( $N + 2) / 2);
} // Driver code $N = 6;
// Function Calling echo nthTerm( $N );
// This code is contributed // by mits ?> |
<script> // JavaScript program to find N-th term of the series: // 1, 4, 15, 72, 420… // Function to find factorial of N function factorial( N)
{ let fact = 1;
for (let i = 1; i <= N; i++)
fact = fact * i;
// return factorial of N
return fact;
} // calculate Nth term of series function nthTerm(N)
{ return (factorial(N) * (N + 2) / 2);
} // Driver code let N = 6;
document.write( nthTerm(N) );
// This code contributed by aashish1995 </script> |
2880
Time Complexity: O(n)
Auxiliary Space: O(1)
Another approach :(Using recursion)
// CPP program to find N-th term of the series: // 1, 4, 15, 72, 420… // Using recursion #include <iostream> using namespace std;
// Function to find factorial of N // with recursion int factorial( int N)
{ // base condition
if ( N == 0 || N == 1 )
return 1;
// use recursion
return N * factorial( N - 1 );
} // calculate Nth term of series int nthTerm( int N)
{ return (factorial(N) * (N + 2) / 2);
} // Driver Function int main()
{ int N = 6;
cout << nthTerm(N);
return 0;
} |
// Java program to find N-th // term of the series: // 1, 4, 15, 72, 420 import java.util.*;
import java.lang.*;
import java.io.*;
class GFG
{ // Function to find factorial of N static int factorial( int N)
{ // base condition
if ( N == 0 || N == 1 )
return 1 ;
// use recursion
return N * factorial( N - 1 );
} // calculate Nth term of series static int nthTerm( int N)
{ return (factorial(N) * (N + 2 ) / 2 );
} // Driver Code public static void main(String args[])
{ int N = 6 ;
System.out.println(nthTerm(N));
} } |
# Python3 program to find # N-th term of the series: # 1, 4, 15, 72, 420… # Using recursion # Function to find factorial # of N with recursion def factorial(N):
# base condition
if N = = 0 or N = = 1 :
return 1
# use recursion
return N * factorial(N - 1 )
def nthTerm(N):
# calculate Nth term of series
return (factorial(N) * (N + 2 ) / / 2 )
# Driver code N = 6
print (nthTerm(N))
# This code is contributed # by Shrikant13 |
// C# program to find N-th // term of the series: // 1, 4, 15, 72, 420 using System;
class GFG
{ // Function to find factorial of N static int factorial( int N)
{ // base condition
if ( N == 0 || N == 1 )
return 1;
// use recursion
return N * factorial( N - 1 );
} // calculate Nth term of series static int nthTerm( int N)
{ return (factorial(N) * (N + 2) / 2);
} // Driver Code public static void Main()
{ int N = 6;
Console.Write(nthTerm(N));
} } // This code is contributed by ChitraNayal |
<?php // PHP program to find // N-th term of the series: // 1, 4, 15, 72, 420… // Function to find factorial // of N with recursion function factorial( $N )
{ // base condition
if ( $N == 0 or $N == 1)
return 1;
// use recursion
return $N * factorial( $N - 1);
} // calculate Nth term of series function nthTerm( $N )
{ return (factorial( $N ) *
( $N + 2) / 2);
} // Driver Code $N = 6;
echo nthTerm( $N );
// This code is contributed // by Shashank ?> |
<script> // Javascript program to find N-th // term of the series: // 1, 4, 15, 72, 420 // Function to find factorial of N function factorial(N)
{ // Base condition
if (N == 0 || N == 1)
return 1;
// Use recursion
return N * factorial(N - 1);
} // Calculate Nth term of series function nthTerm(N)
{ return (factorial(N) * (N + 2) / 2);
} // Driver Code let N = 6; document.write(nthTerm(N)); // This code is contributed by avanitrachhadiya2155 </script> |
2880
Time complexity: O(N)
Auxiliary Space: O(N), for recursion call stack.
Note: Above code wouldn’t work for large values of N. To find the values for large N, use the concept of Factorial for large numbers.