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Sum of the Series `1 + x + x^2 + x^3 + ... + x^n`

Certification: Basic Level Accuracy: 38.46% Submissions: 13 Points: 5

Write a C++ program that calculates the sum of the series `1 + x + x^2 + x^3 + ... + x^n`, where `x` is a real number and `n` is a positive integer provided by the user.

Example 1
    

  • Input: x = 2, n = 3
    • 

  • Output: 15
    • 

  • Explanation: 
      

    • Step 1: Calculate each term in the series: 1 + x + x^2 + x^3.
      • 

    • Step 2: With x = 2 and n = 3: 1 + 2 + 2^2 + 2^3 = 1 + 2 + 4 + 8 = 15.
      • 

    • Step 3: Return 15 as the final sum.
      • 

    •
Example 2
    

  • Input: x = 1.5, n = 4
    • 

  • Output: 13.5625
    • 

  • Explanation: 
      

    • Step 1: Calculate each term in the series: 1 + x + x^2 + x^3 + x^4.
      • 

    • Step 2: With x = 1.5 and n = 4: 1 + 1.5 + 1.5^2 + 1.5^3 + 1.5^4 = 1 + 1.5 + 2.25 + 3.375 + 5.0625 = 13.5625.
      • 

    • Step 3: Return 13.5625 as the final sum.
      • 

    •
Constraints
    

  • 1 ≤ n ≤ 10^6
    • 

  • -100 ≤ x ≤ 100
    • 

  • Time Complexity: O(n)
    • 

  • Space Complexity: O(1)
    •
Variables and Data TypesControl StructuresGoldman SachsZomato
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Hint
Solution

Solution Hints

    
  
  • Use a loop to iterate from 0 to `n`.
    • 
  
  • In each iteration, calculate `x^i` and add it to the sum.
    • 
  
  • Handle edge cases where `x` is 1 separately.
    •

Steps to solve by this approach:

 Step 1: Define a function sum_of_series that takes a double x and an integer n.

 Step 2: Initialize a sum variable to 0.0.

 Step 3: Use a for loop from i=0 to i=n.

 Step 4: For each iteration, add x^i to the sum using pow(x, i).

 Step 5: Return the final sum.

Submitted Code :