Sum of squares of first n natural numbers
The problem at hand involves calculating the sum of the squares of the first n natural numbers. Natural numbers are the positive integers starting from 1. The task is to find the sum of the squares of these natural numbers.
Problem Statement
Given a positive integer n, the objective is to calculate the sum of the squares of the first n natural numbers.
Example
For n = 4, the first n natural numbers are 1, 2, 3, and 4. The squares of these numbers are 1, 4, 9, and 16. The sum of these squares is 1 + 4 + 9 + 16 = 30.
Idea to Solve
To solve this problem, you can either directly calculate the sum using a loop or use a mathematical formula for the
sum of squares. The sum of squares of the first n natural numbers can be calculated using the formula:
sum = n * (n + 1) * (2n + 1) / 6
.
Pseudocode
function squaresOfNaturalNo(n)
sum = n * (n + 1) * (2 * n + 1) / 6
print "Sum of square in", n, "natural numbers is", sum
Algorithm Explanation
- Calculate the sum of the squares of the first n natural numbers using the formula
sum = n * (n + 1) * (2 * n + 1) / 6
. - Print the result.
Code Solution
/*
C program for
Sum of squares of first n natural numbers
*/
#include <stdio.h>
void squaresOfNaturalNo(int n)
{
long long int sum = 0;
if (n > 0)
{
// Normal calculation
// Execute loop 1 to n and calculate squared.
for (int i = 1; i <= n; ++i)
{
// Add square
sum += (i *i);
}
}
printf("\n Sum of square in %d natural number is %lld", n, sum);
}
int main(int argc, char const *argv[])
{
/*
Test A
n = 5
(1)² + (2)² + (3)² + (4)² + (5)² = 55
*/
squaresOfNaturalNo(5);
/*
Test B
n = 8
(1)² + (2)² + (3)² + (4)² + (5)² + (6)² +
(7)² + (8)² = 204
*/
squaresOfNaturalNo(8);
return 0;
}
Output
Sum of square in 5 natural number is 55
Sum of square in 8 natural number is 204
/*
Java program for
Sum of squares of first n natural numbers
*/
public class NaturalNumbers
{
public void squaresOfNaturalNo(int n)
{
long sum = 0;
if (n > 0)
{
// Normal calculation
// Execute loop 1 to n and calculate squared.
for (int i = 1; i <= n; ++i)
{
// Add square
sum += (i * i);
}
}
System.out.print("\n Sum of square in " +
n + " natural number is " + sum);
}
public static void main(String[] args)
{
NaturalNumbers task = new NaturalNumbers();
/*
Test A
n = 5
(1)² + (2)² + (3)² + (4)² + (5)² = 55
*/
task.squaresOfNaturalNo(5);
/*
Test B
n = 8
(1)² + (2)² + (3)² + (4)² + (5)² + (6)² +
(7)² + (8)² = 204
*/
task.squaresOfNaturalNo(8);
}
}
Output
Sum of square in 5 natural number is 55
Sum of square in 8 natural number is 204
// Include header file
#include <iostream>
using namespace std;
/*
C++ program for
Sum of squares of first n natural numbers
*/
class NaturalNumbers
{
public: void squaresOfNaturalNo(int n)
{
long sum = 0;
if (n > 0)
{
// Normal calculation
// Execute loop 1 to n and calculate squared.
for (int i = 1; i <= n; ++i)
{
// Add square
sum += (i *i);
}
}
cout << "\n Sum of square in " << n
<< " natural number is " << sum;
}
};
int main()
{
NaturalNumbers *task = new NaturalNumbers();
/*
Test A
n = 5
(1)² + (2)² + (3)² + (4)² + (5)² = 55
*/
task->squaresOfNaturalNo(5);
/*
Test B
n = 8
(1)² + (2)² + (3)² + (4)² + (5)² + (6)² +
(7)² + (8)² = 204
*/
task->squaresOfNaturalNo(8);
return 0;
}
Output
Sum of square in 5 natural number is 55
Sum of square in 8 natural number is 204
// Include namespace system
using System;
/*
Csharp program for
Sum of squares of first n natural numbers
*/
public class NaturalNumbers
{
public void squaresOfNaturalNo(int n)
{
long sum = 0;
if (n > 0)
{
// Normal calculation
// Execute loop 1 to n and calculate squared.
for (int i = 1; i <= n; ++i)
{
// Add square
sum += (i * i);
}
}
Console.Write("\n Sum of square in " + n +
" natural number is " + sum);
}
public static void Main(String[] args)
{
NaturalNumbers task = new NaturalNumbers();
/*
Test A
n = 5
(1)² + (2)² + (3)² + (4)² + (5)² = 55
*/
task.squaresOfNaturalNo(5);
/*
Test B
n = 8
(1)² + (2)² + (3)² + (4)² + (5)² + (6)² +
(7)² + (8)² = 204
*/
task.squaresOfNaturalNo(8);
}
}
Output
Sum of square in 5 natural number is 55
Sum of square in 8 natural number is 204
package main
import "fmt"
/*
Go program for
Sum of squares of first n natural numbers
*/
func squaresOfNaturalNo(n int) {
var sum int64 = 0
if n > 0 {
// Normal calculation
// Execute loop 1 to n and calculate squared.
for i := 1 ; i <= n ; i++ {
// Add square
sum += int64(i * i)
}
}
fmt.Print("\n Sum of square in ", n,
" natural number is ", sum)
}
func main() {
/*
Test A
n = 5
(1)² + (2)² + (3)² + (4)² + (5)² = 55
*/
squaresOfNaturalNo(5)
/*
Test B
n = 8
(1)² + (2)² + (3)² + (4)² + (5)² + (6)² +
(7)² + (8)² = 204
*/
squaresOfNaturalNo(8)
}
Output
Sum of square in 5 natural number is 55
Sum of square in 8 natural number is 204
<?php
/*
Php program for
Sum of squares of first n natural numbers
*/
class NaturalNumbers
{
public function squaresOfNaturalNo($n)
{
$sum = 0;
if ($n > 0)
{
// Normal calculation
// Execute loop 1 to n and calculate squared.
for ($i = 1; $i <= $n; ++$i)
{
// Add square
$sum += ($i * $i);
}
}
echo("\n Sum of square in ".$n.
" natural number is ".$sum);
}
}
function main()
{
$task = new NaturalNumbers();
/*
Test A
n = 5
(1)² + (2)² + (3)² + (4)² + (5)² = 55
*/
$task->squaresOfNaturalNo(5);
/*
Test B
n = 8
(1)² + (2)² + (3)² + (4)² + (5)² + (6)² +
(7)² + (8)² = 204
*/
$task->squaresOfNaturalNo(8);
}
main();
Output
Sum of square in 5 natural number is 55
Sum of square in 8 natural number is 204
/*
Node JS program for
Sum of squares of first n natural numbers
*/
class NaturalNumbers
{
squaresOfNaturalNo(n)
{
var sum = 0;
if (n > 0)
{
// Normal calculation
// Execute loop 1 to n and calculate squared.
for (var i = 1; i <= n; ++i)
{
// Add square
sum += (i * i);
}
}
process.stdout.write("\n Sum of square in " + n +
" natural number is " + sum);
}
}
function main()
{
var task = new NaturalNumbers();
/*
Test A
n = 5
(1)² + (2)² + (3)² + (4)² + (5)² = 55
*/
task.squaresOfNaturalNo(5);
/*
Test B
n = 8
(1)² + (2)² + (3)² + (4)² + (5)² + (6)² +
(7)² + (8)² = 204
*/
task.squaresOfNaturalNo(8);
}
main();
Output
Sum of square in 5 natural number is 55
Sum of square in 8 natural number is 204
# Python 3 program for
# Sum of squares of first n natural numbers
class NaturalNumbers :
def squaresOfNaturalNo(self, n) :
sum = 0
if (n > 0) :
i = 1
# Normal calculation
# Execute loop 1 to n and calculate squared.
while (i <= n) :
# Add square
sum += (i * i)
i += 1
print("\n Sum of square in",
n ,"natural number is ",
sum, end = "")
def main() :
task = NaturalNumbers()
# Test A
# n = 5
# (1)² + (2)² + (3)² + (4)² + (5)² = 55
task.squaresOfNaturalNo(5)
# Test B
# n = 8
# (1)² + (2)² + (3)² + (4)² + (5)² + (6)² +
# (7)² + (8)² = 204
task.squaresOfNaturalNo(8)
if __name__ == "__main__": main()
Output
Sum of square in 5 natural number is 55
Sum of square in 8 natural number is 204
# Ruby program for
# Sum of squares of first n natural numbers
class NaturalNumbers
def squaresOfNaturalNo(n)
sum = 0
if (n > 0)
i = 1
# Normal calculation
# Execute loop 1 to n and calculate squared.
while (i <= n)
# Add square
sum += (i * i)
i += 1
end
end
print("\n Sum of square in ",
n ," natural number is ", sum)
end
end
def main()
task = NaturalNumbers.new()
# Test A
# n = 5
# (1)² + (2)² + (3)² + (4)² + (5)² = 55
task.squaresOfNaturalNo(5)
# Test B
# n = 8
# (1)² + (2)² + (3)² + (4)² + (5)² + (6)² +
# (7)² + (8)² = 204
task.squaresOfNaturalNo(8)
end
main()
Output
Sum of square in 5 natural number is 55
Sum of square in 8 natural number is 204
/*
Scala program for
Sum of squares of first n natural numbers
*/
class NaturalNumbers()
{
def squaresOfNaturalNo(n: Int): Unit = {
var sum: Long = 0;
if (n > 0)
{
var i: Int = 1;
// Normal calculation
// Execute loop 1 to n and calculate squared.
while (i <= n)
{
// Add square
sum += (i * i);
i += 1;
}
}
print("\n Sum of square in " + n +
" natural number is " + sum);
}
}
object Main
{
def main(args: Array[String]): Unit = {
var task: NaturalNumbers = new NaturalNumbers();
/*
Test A
n = 5
(1)² + (2)² + (3)² + (4)² + (5)² = 55
*/
task.squaresOfNaturalNo(5);
/*
Test B
n = 8
(1)² + (2)² + (3)² + (4)² + (5)² + (6)² +
(7)² + (8)² = 204
*/
task.squaresOfNaturalNo(8);
}
}
Output
Sum of square in 5 natural number is 55
Sum of square in 8 natural number is 204
/*
Swift 4 program for
Sum of squares of first n natural numbers
*/
class NaturalNumbers
{
func squaresOfNaturalNo(_ n: Int)
{
var sum: Int = 0;
if (n > 0)
{
var i: Int = 1;
// Normal calculation
// Execute loop 1 to n and calculate squared.
while (i <= n)
{
// Add square
sum += (i * i);
i += 1;
}
}
print("\n Sum of square in", n ,
"natural number is ", sum, terminator: "");
}
}
func main()
{
let task: NaturalNumbers = NaturalNumbers();
/*
Test A
n = 5
(1)² + (2)² + (3)² + (4)² + (5)² = 55
*/
task.squaresOfNaturalNo(5);
/*
Test B
n = 8
(1)² + (2)² + (3)² + (4)² + (5)² + (6)² +
(7)² + (8)² = 204
*/
task.squaresOfNaturalNo(8);
}
main();
Output
Sum of square in 5 natural number is 55
Sum of square in 8 natural number is 204
/*
Kotlin program for
Sum of squares of first n natural numbers
*/
class NaturalNumbers
{
fun squaresOfNaturalNo(n: Int): Unit
{
var sum: Long = 0;
if (n > 0)
{
var i: Int = 1;
// Normal calculation
// Execute loop 1 to n and calculate squared.
while (i <= n)
{
// Add square
sum += (i * i);
i += 1;
}
}
print("\n Sum of square in " + n +
" natural number is " + sum);
}
}
fun main(args: Array < String > ): Unit
{
val task: NaturalNumbers = NaturalNumbers();
/*
Test A
n = 5
(1)² + (2)² + (3)² + (4)² + (5)² = 55
*/
task.squaresOfNaturalNo(5);
/*
Test B
n = 8
(1)² + (2)² + (3)² + (4)² + (5)² + (6)² +
(7)² + (8)² = 204
*/
task.squaresOfNaturalNo(8);
}
Output
Sum of square in 5 natural number is 55
Sum of square in 8 natural number is 204
Time Complexity
The time complexity of this algorithm is O(n), as it involves a loop that iterates from 1 to n to calculate the sum. The space complexity is constant, as it uses a fixed number of variables regardless of the input size.
Please share your knowledge to improve code and content standard. Also submit your doubts, and test case. We improve by your feedback. We will try to resolve your query as soon as possible.
New Comment