Average of Squares of Natural Numbers
Given a number n, find the average of square of natural Numbers till n
Examples :
Input : n = 2 Output :2.5 12 + 22 = 2.5 Input : n = 3 Output : 4.666667 12 + 22 + 32 = 4.666667
Naive approach :
A naive approach will be to run a loop from 1 to n and and find the average of sum up all the squares.
C
// C program to calculate 1^2+2^2+3^2+... average // of square number #include <stdio.h> // 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; } |
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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. |
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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 = 2print (AvgofSquareN(n)) # This code is contributed by # Manish Shaw(manishshaw1) |
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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. |
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PHP
<?php // PHP program to calculate 1^2+2^2+3^2+... // average of square number // Function to calculate average // of square number function AvgofSquareN( $n) { $sum = 0; for ($i = 1; $i <= $n; $i++) $sum += ($i * $i); return $sum/$n; } // Driver code $n = 2; echo(AvgofSquareN($n)); // This code is contributed by vt_m. ?> |
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Output :
2.500000
Efficient Approach : Sum of squares of natural numbers (n + 1)(2n + 1) / 6. Therefore average is 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 <stdio.h> 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; } |
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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. |
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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) |
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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. |
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PHP
<?php // PHP program to get the Average of // Square of first n natural numbers function AvgofSquareN( $n) { return (($n + 1) * (2 * $n + 1)) / 6; } // Driver Code $n = 2; echo(AvgofSquareN($n)); // This code is contributed by vt_m. ?> |
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Output :
2.500000
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