Question

Write a program that prints the sum of the first ten positive integers, \(1+2+\ldots+10\).

Short answer

The sum of the first ten positive integers is 55.

Step-by-step solution

Understand the Problem

We need to write a program that calculates and prints the sum of the first ten positive integers. These integers are 1 through 10.

Choose a Programming Language

We will use Python as the programming language for this task due to its simplicity and readability.

Initialize a Sum Variable

In the program, we will need a variable to store the sum as we calculate it. We'll start by setting this variable to zero.

Loop Through the First Ten Integers

We will use a loop to iterate through the numbers 1 to 10. For each number, we'll add it to our sum variable.

Print the Result

After the loop has added all numbers from 1 to 10, we will print the value of the sum variable to display the result.

Write the Python Code

The code for this task in Python is: ```python sum_of_integers = 0 for i in range(1, 11): sum_of_integers += i print(sum_of_integers) ```

Key concepts

Loops

In programming, loops allow us to repeat a set of instructions until a specific condition is met. This is particularly helpful when we want to perform repetitive tasks, like adding a series of numbers together.

Python provides several types of loops, with the most common being the 'for' and 'while' loops. In our exercise, a 'for' loop is best suited as it helps iterate through a sequence of numbers directly. The loop in our solution is `for i in range(1, 11):`, which systematically goes through each number from 1 to 10.

• The `range()` function is key here. It generates a sequence of numbers, in this case, starting from 1 up to, but not including, 11.
• The loop variable `i` takes on each value in this range, allowing us to perform operations on each one in turn.

Loops reduce the complexity of a program and help manage repetitive tasks efficiently.

Variables

Variables are essentially containers for storing data values. They allow us to hold and manipulate information within programs.

In Python, creating a variable is straightforward — you just need to assign a value to a name using the equal sign (`=`). In our example `sum_of_integers = 0`, we initiated a variable named `sum_of_integers` to store the cumulative sum of integers from 1 to 10. Here’s why:

• By initializing this variable to 0, we ensure that our calculations begin from a neutral starting point.
• Variables can change as the program runs, allowing dynamic data manipulation.
• Each time the loop runs, the current number is added to `sum_of_integers` using the `+=` operator, which is shorthand for updating the variable’s value."

Variables form the backbone of any program by allowing data to be accessed and modified as needed.

Control Structures

Control structures, such as loops and conditionals, direct the flow of a program by determining which blocks of code to execute.

The 'if-else' condition and loops are classic examples of control structures, enabling decision-making and repetition. In our exercise, the primary control structure used is the 'for' loop: `for i in range(1, 11):`.

• This loop, as a control structure, dictates that the block of code within it runs 10 times, corresponding to the numbers 1 through 10.
• Control structures transform linear code into a flexible sequence of operations, following logical pathways defined by the programmer.

These structures are critical in Python for efficient execution flow management, making it possible to automate repetitive tasks and complex decision-making.

Basic Arithmetic Operations

Arithmetic operations are the backbone of most programming tasks involving mathematical calculations. These operations include addition, subtraction, multiplication, and division.

In our exercise, we focused on addition, which is implemented using the `+` operator. This is the simplest form of arithmetic, yet powerful when used in conjunction with loops and variables.

• Each time the loop iterates, the current integer is added to our variable `sum_of_integers`.
• The `+=` operator is shorthand for accumulating the total sum, meaning `sum_of_integers += i` is a quick way to write `sum_of_integers = sum_of_integers + i`.
• Basic arithmetic in Python is straightforward, thanks to the use of clear and concise operators.

Mastering these operations and understanding their use within loops and control structures is fundamental to programming efficiently in Python.