Mastering the Sum of Series in C++

Introduction

In this lab, we will learn how to write a C++ program that finds the sum of the series 1 + 2 + 4 + 8 + 16 + 32 + ... + n. We will use two different approaches. The first approach uses a for loop to add values in the sequence, while the second approach uses a mathematical formula to calculate the sum.

Create a new file

First, let's open the terminal and navigate to the ~/project directory. In this directory, create a new file called main.cpp. We can do this using the following command:

touch ~/project/main.cpp

Next, open the file in your favorite text editor.

Using a for loop

In this approach, we use a for loop to iterate through the sequence and add up the numbers from 1 to n. We will store the sum in a variable called sum.

Add the following code to your main.cpp file:

#include <iostream>

int main() {
    int n, sum = 0;
    std::cout << "Enter the value of n: ";
    std::cin >> n;

    for(int i = 1; i <= n; ++i) {
        sum += i;
    }

    std::cout << "The sum of the sequence is: " << sum << std::endl;

    return 0;
}

Here, we use the std::cout function to display a message asking the user to enter the value of n. We then use the std::cin function to read in the value of n entered by the user. We initialize sum to 0 before starting the for loop.

The for loop iterates over values of i from 1 to n, adding each value to the sum. Finally, we display the sum using std::cout.

Before we can run the program, we need to compile it. In the terminal, navigate to the ~/project directory and run the following command:

g++ main.cpp -o main && ./main

This will compile and run the program. You should see a message asking you to enter the value of n. After you enter a value, the program will display the sum of the sequence.

Using a mathematical formula

In this approach, we use a mathematical formula to calculate the sum of the sequence. The formula is sum = 2^n - 1, where n is the number of terms in the sequence.

Add the following code to your main.cpp file:

#include <iostream>
#include <cmath>

int main() {
    int n;
    std::cout << "Enter the value of n: ";
    std::cin >> n;

    int sum = pow(2, n) - 1;

    std::cout << "The sum of the sequence is: " << sum << std::endl;

    return 0;
}

Here, we use the std::pow function to calculate 2^n. We subtract 1 from this value to get the sum of the sequence. We then display the sum using std::cout.

Before we can run the program, we need to compile it. In the terminal, navigate to the ~/project directory and run the following command:

g++ main.cpp -o main && ./main

This will compile and run the program. You should see a message asking you to enter the value of n. After you enter a value, the program will display the sum of the sequence.

Full code

Here is the full code for main.cpp:

#include <iostream>
#include <cmath>

int main() {
    int n;
    std::cout << "Enter the value of n: ";
    std::cin >> n;

    int sum = pow(2, n) - 1;

    std::cout << "The sum of the sequence is: " << sum << std::endl;

    return 0;
}

#include <iostream>

int main() {
    int n, sum = 0;
    std::cout << "Enter the value of n: ";
    std::cin >> n;

    for(int i = 1; i <= n; ++i) {
        sum += i;
    }

    std::cout << "The sum of the sequence is: " << sum << std::endl;

    return 0;
}

Summary

In this lab, we learned how to write a C++ program to find the sum of the series 1 + 2 + 4 + 8 + 16 + 32 + ... + n. We used two different approaches - one using a for loop and another using a mathematical formula. You can use either of these methods to find the sum of any arithmetic sequence.

Find the Sum of Series