Step 1: Understanding the Problem

We need to generate a list of triangular numbers within a given range. A triangular number is defined as n(n+1)/2 for n being any natural number. This means it is essentially the sum of all numbers up to a certain number n.

let n = 5
let triangularNumber = n * (n + 1) / 2

Step 2: Setting Up the Function

We set up a function called findTriangularNumbers which accepts two arguments - the lower limit start and the upper limit end of our range.

func findTriangularNumbers(start: Int, end: Int) -> [Int] {
    var result = [Int]()
    return result
}

Step 3: Generating Triangular Numbers

Within the function, we iterate from start to end. For each number, we'll check if it's a triangular number by reversing the formula to sqrt(8 * x + 1) - 1 / 2.

for number in start...end {
    let n = (sqrt(1 + 8 * Double(number)) - 1) / 2
    if n == floor(n) {
        result.append(number)
    }
}

Step 4: Return the Result

The function will then return the result list which contains all triangular numbers in the provided range.

return result

Conclusion

Here is the complete function implementation for finding all triangular numbers within a given range.

import Foundation

func findTriangularNumbersRange(start: Int, end: Int) -> [Int] {
    var result = [Int]()
    for number in start...end {
        let n = (sqrt(1 + 8 * Double(number)) - 1) / 2
        if n == floor(n) {
            result.append(number)
        }
    }
    return result
}