Как найти сумму квадратов чисел в питоне

In this tutorial, you will learn how to create a program to calculate the sum of squares of first N natural numbers. To execute this program, we will be using the concept of loops in Python. You must know this concept before moving further.

For a positive integer N, the task is to find the value of,

1² + 2² + 3² + 4².....+ N²

The program should accept the following input, look at the sample input and output below,

Input– enter n: 13

Output– sum of square of first 13 natural numbers: 819

For executing this task, we can follow two approaches:

1. Using loops
2. Using formula

Approach 1: Using loops

In this approach, we will use the concept of loops to find the squares of the first n numbers and we will keep on adding the numbers to get the final sum.

Algorithm

Step 1– Define a function to find the sum of squares

Step 2– Declare a variable that will store the sum

Step 3– Define a loop that will run n times

Step 4– Inside the loop update the value of the variable which will store the sum of squares

Step 5– Calculate the square of each number before adding it to the sum

Step 6- Return the value of s

Step 7- Take input of n from the user

Step 8- Pass the input as a parameter in the function

Step 9– Display the result returned by the function

Python Program 1

Look at the complete program given below to understand the implementation of the approach.

def SumofSquares(n):
    s=0
    for i in range(n+1):
        s+=i**2
    return s

#input
n=int(input("enter n: "))
print("sum of squares of first {} natural numbers: ".format(n),SumofSquares(n))

enter n: 20
sum of squares of first 20 natural numbers: 2870

The operator ** is used to calculate exponents, i**2 is the same as i²

The format() is a function for handling strings that permits you to do variable substitutions and data formatting. Here, we have used this function to print the value of n in place of {} in the print statement.

Approach 2: Using Formula

In mathematics, there is a formula to calculate the sum of squares of first n numbers. We can directly put this formula to calculate our result. This will eliminate the need for a loop in our program.

sum of squares of first n natural numbers = (n*(n+1)*(2n+1))/6

Algorithm

Step 1- Define a function to calculate the sum of squares

Step 2- Use the formula mentioned above to calculate the sum of squares of n natural numbers

Step 3– Return the value calculated above

Step 4– Take input of n from the user

Step 5– Call the function to display the result

Python Program 2

Look at the complete program given below to understand the implementation of the approach.

def SquareSum(n) :
    return (n * (n + 1) * (2 * n + 1)) // 6
  
n=int(input("enter N: "))
print("Sum of squares of first {} natural numbers: ".format(n),SquareSum(n))

enter N: 10
Sum of squares of first 10 natural numbers: 385

The format() function is used in the same way as mentioned above to display the value of n in place of {} in the print statement.

Conclusion

In this tutorial, we have learned two ways by which we can calculate the sum of the squares of the first N natural numbers. One is by using a loop that will calculate the squares of N numbers and add them up to give the final result. Second, we can directly use the formula to get the value of the sum of the squares of N natural numbers.