C++ Exercises: Display the sum of the series 1+x+x^2/2!+x^3/3!+....

Last update on April 07 2025 13:01:27 (UTC/GMT +8 hours)

24. Sum of the Series [1 + x + x^2/2! + x^3/3! + ...]

Write a program in C++ to display the sum of the series [ 1+x+x^2/2!+x^3/3!+....].

Sample Solution:

C++ Code :

#include <iostream> // Including input-output stream header

using namespace std; // Using standard namespace to avoid writing std::

int main() // Start of the main function
{
    float x, sum, no_row; // Declaration of float variables 'x' (input value), 'sum' (to store the sum), 'no_row' (value of the current term)
    int i, n; // Declaration of integer variables 'i' (loop counter), 'n' (number of terms)

    cout << "\n\n Display the sum of the series [ 1+x+x^2/2!+x^3/3!+....]\n"; // Displaying a message on the console
    cout << "------------------------------------------------------------\n";
    cout << " Input the value of x: "; // Prompting the user to input the value of x
    cin >> x; // Reading the input value as 'x'

    cout << " Input number of terms: "; // Prompting the user to input the number of terms
    cin >> n; // Reading the input value as the number of terms

    sum = 1; // Initializing 'sum' with the first term of the series (1)
    no_row = 1; // Initializing 'no_row' with the first term (1)

    for (i = 1; i < n; i++) // Loop to calculate 'n' terms of the series
    {
        no_row = no_row * x / (float)i; // Calculating the value of the current term based on the formula
        sum = sum + no_row; // Adding the current term to the sum
    }

    cout << " The sum is : " << sum << endl; // Displaying the sum of the series
}

Sample Output:

 Display the sum of the series [ 1+x+x^2/2!+x^3/3!+....]               
------------------------------------------------------------           
 Input the value of x: 3                                               
 Input number of terms: 5                                              
 The sum  is : 16.375

Flowchart:

For more Practice: Solve these Related Problems:

Write a C++ program to calculate the sum of the exponential series for a given x and n terms using a loop.
Write a C++ program that computes the series 1 + x + x^2/2! + ... up to n terms and displays each term’s value.
Write a C++ program to evaluate the series for e^x using a for loop, printing both individual terms and the final sum.
Write a C++ program that reads x and n, then computes the sum of the power series with factorial denominators, displaying the result.

C++ Code Editor:

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