级数之和(n ^ 2-1 ^ 2)+ 2(n ^ 2-2 ^ 2)+….n(n ^ 2-n ^ 2)

查找序列第n个项之和的程序(n ^ 2-1 ^ 2)+ 2(n ^ 2-2 ^ 2)+ 3(n ^ 2-3 ^ 2)+….n(n ^ 2-n ^ 2)
例子：

Input : 2
Output :3

Input :5
Output :150

为了解决该问题，我们具有公式((1/4)* n ² *(n ² -1))。我们可以使用数学归纳法证明该公式。

Example n = 2
result = ((1/4)*2^2*(2^2-1))
       = ((0.25)*4*(4-1))
       = ((0.25)*4*3
       = 3 ans.

C++

// CPP Program to finding the
// sum of the nth series
#include 
using namespace std;
 
// function that calculate
// the sum of the nth series
int sum_series(int n)
{
    int nSquare = n * n;
 
    // using formula of the nth term
    return nSquare * (nSquare - 1) / 4;
}
 
// driver function
int main()
{
    int n = 2;
    cout << sum_series(n) << endl;
    return 0;
}

Java

// javaProgram to finding the
// sum of the nth series
import java.io.*;
 
class GFG {
     
    // function that calculate
    // the sum of the nth series
    static int sum_series(int n)
    {
        int nSquare = n * n;
     
        // using formula of the nth term
        return nSquare * (nSquare - 1) / 4;
    }
 
    // Driver function
    public static void main (String[] args)
    {
        int n = 2;
        System.out.println( sum_series(n)) ;
     
    }
     
}
// This article is contributed by vt_m

Python3

# Python 3 Program to finding
# the sum of the nth series
 
# function that calculate
# the sum of the nth series
def sum_series(n):
 
    nSquare = n * n
 
    # Using formula of the
    # nth term
    return int(nSquare * (nSquare - 1) / 4)
 
# Driver function
n = 2
print(sum_series(n))
 
# This code is contributed by Smitha Dinesh Semwal

C#

// C# program to finding the
// sum of the nth series
using System;
 
class GFG {
     
    // Function that calculate
    // the sum of the nth series
    static int sum_series(int n)
    {
        int nSquare = n * n;
     
        // Using formula of the nth term
        return nSquare * (nSquare - 1) / 4;
    }
 
    // Driver Code
    public static void Main ()
    {
        int n = 2;
        Console.Write( sum_series(n)) ;
     
    }
}
 
// This code is contributed by vt_m

Javascript

 
// JavaScript Program to finding the
// sum of the nth series
 
    // function that calculate
    // the sum of the nth series
    function sum_series(n)
    {
        let nSquare = n * n;
       
        // using formula of the nth term
        return nSquare * (nSquare - 1) / 4;
    }
   
  
// Driver code
 
        let n = 2;
        document.write( sum_series(n)) ;
 

输出：

3