给定一个数字N。任务是编写一个程序来查找N th 以下系列中的术语：
null
1, 4, 15, 72, 420…
例如：
Input: 3Output: 15For N = 3, we know that the factorial of 3 is 6Nth term = 6*(3+2)/2 = 15Input: 6Output: 2880For N = 6, we know that the factorial of 6 is 720Nth term = 620*(6+2)/2 = 2880
其思想是首先找到给定数N的阶乘，即N！。现在，上述系列中的第N项将是：
第N项 =N！*（N+2）/2
以下是上述方法的实施情况：
C++
// 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
// 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 |
Python3
# 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#
// 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 // 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 ?> |
Javascript
<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> |
输出：
2880
另一种方法： （使用递归）
C++
// 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
// 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
# 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#
// 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 // 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 ?> |
Javascript
<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> |
输出：
2880
时间复杂性 ：O（N） 注： 上述代码不适用于较大的N值。要查找较大的N值，请使用 大数的阶乘。
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