自然数平方的平均值

给定一个数n，找到直到n的自然数平方的平均值
例子 ：

Input : n = 2
Output :2.5
12 + 22 = 2.5

Input  : n = 3
Output : 4.666667
12 + 22 + 32 = 4.666667

天真的方法：
天真的方法是从1到n循环，然后求出所有平方之和的平均值。

C

// C program to calculate 1^2+2^2+3^2+... average
// of square number
#include 
 
// Function to calculate  average of square number
float AvgofSquareN(int n)
{
    float sum = 0;
    for (int i = 1; i <= n; i++)
        sum += (i * i);
    return sum/n;
}
 
// Driver code
int main()
{
    int n = 2;
    printf("%f", AvgofSquareN(n));
    return 0;
}

C++

// C++ program to calculate 1^2+2^2+3^2+...
// average of square number
#include
using namespace std;
 
// Function to calculate average of squares
float AvgofSquareN(int n)
{
    float sum = 0;
    for (int i = 1; i <= n; i++)
        sum += (i * i);
    return sum/n;
}
 
// Driver code
int main()
{
    int n = 2;
    cout << AvgofSquareN(n) ;
    return 0;
}

Java

// Java program to calculate 1^2+2^2+3^2+
// ... average of square number
import java.io.*;
 
public class GFG{
     
// Function to calculate average
// of square number
static float AvgofSquareN(int n)
{
    float sum = 0;
    for (int i = 1; i <= n; i++)
        sum += (i * i);
    return sum / n;
}
 
// Driver code
static public void main (String[] args)
{
    int n = 2;
    System.out.println(AvgofSquareN(n));
 
}
}
 
// This code is contributed by vt_m.

Python3

# Python program to
# calculate 1^2+2^2+3^2+...
# average of square number
 
# Function to calculate
# average of square number
def AvgofSquareN(n) :
 
    sum = 0
    for i in range(1, n + 1) :
        sum += (i * i)
    return sum/n
 
# Driver code
n = 2
print (AvgofSquareN(n))
     
# This code is contributed by
# Manish Shaw(manishshaw1)

C#

// C# program to calculate 1^2+2^2+3^2+
// ... average of square number
using System;
 
public class GFG{
     
 
// Function to calculate average
// of square number
static float AvgofSquareN(int n)
{
    float sum = 0;
    for (int i = 1; i <= n; i++)
        sum += (i * i);
    return sum / n;
}
 
// Driver code
static public void Main (String []args)
{
    int n = 2;
    Console.WriteLine(AvgofSquareN(n));
     
}
}
 
// This code is contributed by vt_m.

Javascript

// javascript program to calculate 1^2+2^2+3^2+... average
// of square number
 
// Function to calculate  average of square number
function AvgofSquareN( n)
{
    let sum = 0;
    for (let i = 1; i <= n; i++)
        sum += (i * i);
    return sum/n;
}
 
// Driver code
    let n = 2;
    document.write(AvgofSquareN(n).toFixed(6));
 
// This code is contributed by todaysgaurav
 

输出 ：

2.500000

时间复杂度： O(n)
空间复杂度： O(1)
有效方法：自然数的平方和(n + 1)(2n +1)/ 6 。因此平均值为n(n +1)(2n +1)/ 6 * n =(n +1)(2n +1)/ 6

C

// C program to get the  Average of Square
// of first n natural numbers
#include 
 
float AvgofSquareN(int n)
{
    return (float)((n + 1) * (2 * n + 1)) / 6;
}
 
// Driver Code
int main()
{
    int n = 10;
    printf("%f", AvgofSquareN(n));
    return 0;
}

C++

// C++ program to get the  Average of Square
// of first n natural numbers
#include
using namespace std;
 
float AvgofSquareN(int n)
{
    return (float)((n + 1) * (2 * n + 1)) / 6;
}
 
// Driver Code
int main()
{
    int n = 10;
    cout << AvgofSquareN(n) ;
    return 0;
}

Java

// Java program to get the Average of
// square of first n natural numbers
import java.io.*;
 
public class GFG{
 
// Function to get the average
static float AvgofSquareN(int n)
{
    return (float)((n + 1) * (2 *
                    n + 1)) / 6;
}
 
// Driver Code
static public void main (String[] args)
{
    int n = 2;
    System.out.println(AvgofSquareN(n));
 
}
}
 
// This code is contributed by vt_m. 

Python3

# PHP program to get the Average of
# Square of first n natural numbers
  
def AvgofSquareN(n) :
 
    return ((n + 1) * (2 * n + 1)) / 6;
 
# Driver Code
n = 2;
print (AvgofSquareN(n));
  
# This code is contributed by Manish Shaw
# (manishshaw1)

C＃

// C# program to get the Average of
// squareof first n natural numbers
using System;
 
public class GFG{
 
// Function to calculate average
static float AvgofSquareN(int n)
{
    return (float)((n + 1) * (2 *
                    n + 1)) / 6;
}
 
// Driver Code
static public void Main (String []args)
{
    int n = 2;
    Console.WriteLine(AvgofSquareN(n));
}
}
 
// This code is contributed by vt_m.

Java脚本

// javascript program to get the Average of
// square of first n natural numberspublic
 
// Function to get the average
function AvgofSquareN(n)
{
    return ((n + 1) * (2 *
                    n + 1)) / 6;
}
 
// Driver Code
var n = 2;
document.write(AvgofSquareN(n));
 
 
// This code is contributed by Amit Katiyar

2.500000

时间复杂度： O(1)
空间复杂度： O(1)