系列的总和1 +(1 + 2)+(1 + 2 + 3)+(1 + 2 + 3 + 4)+……+(1 + 2 + 3 + 4 +…+ n)

给定n的值，我们需要找到级数之和，其中第i个项是第i个自然数的和。
例子 ：

Input  : n = 5   
Output : 35
Explanation :
(1) + (1+2) + (1+2+3) + (1+2+3+4) + (1+2+3+4+5) = 35

Input  : n = 10
Output : 220
Explanation :
(1) + (1+2) + (1+2+3) +  .... +(1+2+3+4+.....+10) = 220

天真的方法：
以下是上述系列的实现：

C++

// CPP program to find sum of given series
#include 
using namespace std;
 
// Function to find sum of given series
int sumOfSeries(int n)
{
    int sum = 0;
    for (int i = 1 ; i <= n ; i++)
        for (int j = 1 ; j <= i ; j++)
            sum += j;
    return sum;
}
 
// Driver Function
int main()
{
    int n = 10;
    cout << sumOfSeries(n);
    return 0;
}

Java

// JAVA Code For Sum of the series
import java.util.*;
 
class GFG {
     
    // Function to find sum of given series
    static int sumOfSeries(int n)
    {
        int sum = 0;
        for (int i = 1 ; i <= n ; i++)
            for (int j = 1 ; j <= i ; j++)
                sum += j;
        return sum;
    }
     
    /* Driver program to test above function */
    public static void main(String[] args)
    {
         int n = 10;
         System.out.println(sumOfSeries(n));
         
    }
}
 
// This code is contributed by Arnav Kr. Mandal.

Python

# Python3 program to find sum of given series
 
# Function to find sum of series
def sumOfSeries(n):
    return sum([i*(i+1)/2 for i in range(1, n + 1)])
 
# Driver Code
if __name__ == "__main__":
    n = 10
    print(sumOfSeries(n))

C#

// C# Code For Sum of the series
using System;
 
class GFG {
 
    // Function to find sum of given series
    static int sumOfSeries(int n)
    {
        int sum = 0;
        for (int i = 1; i <= n; i++)
            for (int j = 1; j <= i; j++)
                sum += j;
        return sum;
    }
 
    /* Driver program to test above function */
    public static void Main()
    {
        int n = 10;
         
        Console.Write(sumOfSeries(n));
    }
}
 
// This code is contributed by vt_m.

Javascript

 
// JavaScript Program for Sum of the series
 
 // Function to find sum of given series
    function sumOfSeries(n)
    {
        let sum = 0;
        for (let i = 1 ; i <= n ; i++)
            for (let j = 1 ; j <= i ; j++)
                sum += j;
        return sum;
    }
 
// Driver code   
          
        let n = 10;
        document.write(sumOfSeries(n));
             

输出 ：

220

高效的方法：
让$n^{th}$系列1 +(1 + 2)+(1 + 2 + 3)+(1 + 2 + 3 + 4)…(1 + 2 + 3 + .. n)的项表示为_n

_正^{=ΣN +} ₁ $i$ = $\frac{n (n + 1)}{2}$ = $\frac{(n^2 + n)}{2}$系列∑ ⁿ ₁ a _n = ∑ ⁿ ₁的n个项之和$\frac{(n^2 + n)}{2}$ = $\frac{1}{2}$ Σ $[$$n^2$$]$ +Σ $[$$n$$]$ = $\frac{1}{2}$ * $\frac{n(n + 1)(2n + 1)}{6}$ + $\frac{1}{2}$ * $\frac{n(n+1)}{2}$ = $\frac{n(n+1)(2n+4)}{12}$

下面是上述方法的实现：

C++

// CPP program to find sum of given series
#include 
using namespace std;
 
// Function to find sum of given series
int sumOfSeries(int n)
{
    return (n * (n + 1) * (2 * n + 4)) / 12;
}
 
// Driver Function
int main()
{
    int n = 10;
    cout << sumOfSeries(n);
}

Java

// JAVA Code For Sum of the series
import java.util.*;
 
class GFG {
     
    // Function to find sum of given series
    static int sumOfSeries(int n)
    {
        return (n * (n + 1) *
                (2 * n + 4)) / 12;
    }
     
    /* Driver program to test above function */
    public static void main(String[] args)
    {
         int n = 10;
         System.out.println(sumOfSeries(n));
         
    }
}
 
// This code is contributed by Arnav Kr. Mandal.

Python

# Python program to find sum of given series
 
# Function to find sum of given series
def sumOfSeries(n):
    return (n * (n + 1) * (2 * n + 4)) / 12;
     
# Driver function
if __name__ == '__main__':
    n = 10
    print(sumOfSeries(n))

C＃

// C# Code For Sum of the series
using System;
 
class GFG {
 
    // Function to find sum of given series
    static int sumOfSeries(int n)
    {
        return (n * (n + 1) * (2 * n + 4)) / 12;
    }
 
    /* Driver program to test above function */
    public static void Main()
    {
        int n = 10;
         
        Console.Write(sumOfSeries(n));
    }
}
 
// This code is contributed by vt_m.

Java脚本

 
// JavaScript program For Sum of the series
 
// Function to find sum of given series
    function sumOfSeries(n)
    {
        return (n * (n + 1) *
                (2 * n + 4)) / 12;
    }
      
 
// Driver code
         
        let n = 10;
        document.write(sumOfSeries(n));
                   

输出 ：

220