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Sum of the Series 1² + 2² + ... + n²

Certification: Basic Level Accuracy: 44.44% Submissions: 9 Points: 5

Write a C++ program to calculate the sum of the series 1² + 2² + 3² + ... + n², where n is a positive integer.

Example 1
    

  • Input: n = 5
    • 

  • Output: 55
    • 

  • Explanation: 
      

    • Step 1: Calculate the sum of squares from 1 to 5: 1² + 2² + 3² + 4² + 5².
      • 

    • Step 2: 1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25.
      • 

    • Step 3: Sum = 1 + 4 + 9 + 16 + 25 = 55.
      • 

    • Step 4: Alternatively, use the formula: sum = n(n+1)(2n+1)/6 = 5(5+1)(2×5+1)/6 = 5×6×11/6 = 55.
      • 

    •
Example 2
    

  • Input: n = 10
    • 

  • Output: 385
    • 

  • Explanation: 
      

    • Step 1: Calculate the sum of squares from 1 to 10: 1² + 2² + 3² + ... + 10².
      • 

    • Step 2: 1² = 1, 2² = 4, ..., 10² = 100.
      • 

    • Step 3: Sum = 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 = 385.
      • 

    • Step 4: Alternatively, use the formula: sum = n(n+1)(2n+1)/6 = 10(10+1)(2×10+1)/6 = 10×11×21/6 = 385.
      • 

    •
Constraints
    

  • 1 ≤ n ≤ 10^4
    • 

  • Time Complexity: O(1) or O(n)
    • 

  • Space Complexity: O(1)
    •
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Hint
Solution

Solution Hints

    
  
  • Use the mathematical formula for the sum of squares: n(n+1)(2n+1)/6.
    • 
  
  • Alternatively, you can iterate through each number and add its square to the sum.
    • 
  
  • Be careful about integer overflow for larger values of n.
    • 
  
  • For large values of n, consider using a long long int data type.
    •

Steps to solve by this approach:

 Step 1: Define a function sumOfSquareSeries that takes an integer n.

 Step 2: Apply the mathematical formula: n(n+1)(2n+1)/6 to calculate the sum directly.

 Step 3: Return the calculated sum.

 Step 4: (Alternative approach) Initialize a sum variable to 0.

 Step 5: (Alternative approach) Use a for loop from i=1 to i=n.

 Step 6: (Alternative approach) For each iteration, add i^2 to the sum.

 Step 7: (Alternative approach) Return the final sum.

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