求出2 * 3 * 5、3 * 5 * 7、4 * 7 * 9，…的序列的前N个项的总和。

给定整数N ，任务是找到该系列的前N个项的总和：

(2 * 3 * 5), (3 * 5 * 7), (4 * 7 * 9), … 
 

例子：

Input: N = 3 
Output: 387 
S₃ = (2 * 3 * 5) + (3 * 5 * 7) + (4 * 7 * 9) = 30 + 105 + 252 = 387
Input: N = 5 
Output: 1740 
 

方法：让级数的^第N^个为T _n 。通过观察序列的^第N^个项，可以很容易地找到该序列的总和：

T_n = {n^th term of 2, 3, 4, …} * {n^th term of 3, 5, 7, …} * {n^th term of 5, 7, 9, …} 
T_n = (n + 1) * (2 * n + 1) * (2* n + 3) 
T_n = 4n³ + 12n² + 11n + 3 
 

前n个项的和( S _n )可以通过

S_n = ΣT_n 
S_n = Σ[4n³ + 12n² + 11n + 3] 
S_n = (n / 2) * [2n³ + 12n² + 25n + 21] 
 

下面是上述方法的实现：

C++

// C++ program to find sum of the
// first n terms of the given series
#include 
using namespace std;
 
// Function to return the sum of the
// first n terms of the given series
int calSum(int n)
{
    // As described in the approach
    return (n * (2 * n * n * n + 12 * n * n + 25 * n + 21)) / 2;
}
 
// Driver code
int main()
{
    int n = 3;
    cout << calSum(n);
    return 0;
}

Java

// Java program to find sum of the
// first n terms of the given series
class GFG {
 
    // Function to return the sum of the
    // first n terms of the given series
    static int calSum(int n)
    {
 
        // As described in the approach
        return (n * (2 * n * n * n + 12 * n * n + 25 * n + 21)) / 2;
    }
 
    // Driver Code
    public static void main(String args[])
    {
        int n = 3;
        System.out.println(calSum(n));
    }
}

Python

# C++ program to find sum of the
# first n terms of the given series
 
# Function to return the sum of the
# first n terms of the given series
def calSum(n):
     
    # As described in the approach
    return (n*(2 * n*n * n + 12 * n*n + 25 * n + 21))/2;
 
# Driver Code
n = 3
print(calSum(n))

C#

// C# program to find sum of the
// first n terms of the given series
using System;
 
class GFG {
 
    // Function to return the sum of the
    // first n terms of the given series
    static int calSum(int n)
    {
 
        // As described in the approach
        return (n * (2 * n * n * n + 12 * n * n + 25 * n + 21)) / 2;
    }
 
    // Driver code
    static public void Main()
    {
        int n = 3;
        Console.WriteLine(calSum(n));
    }
}

Javascript

// Javascript program to find sum of the
// first n terms of the given series
 
    // Function to return the sum of the
    // first n terms of the given series
    function calSum( n) {
 
        // As described in the approach
        return (n * (2 * n * n * n + 12 * n * n + 25 * n + 21)) / 2;
    }
 
    // Driver Code
    let n = 3;
    document.write(calSum(n));
 
// This code is contributed by 29AjayKumar

输出：

387