1. To provide a detailed explanation without using sigma notation, I will break down the process into clear, numbered steps. 2. Sigma notation ($\sum$) is a compact way of representing the sum of a series of terms, but here we will manually handle each term and add them step-by-step. 3. For example, if you wanted to find the sum of the first 5 natural numbers, instead of writing $\sum_{i=1}^{5} i$, we list and add each term: 4. Step 1: Start with the first number: 1. 5. Step 2: Add the second number: $1 + 2 = 3$. 6. Step 3: Add the third number: $3 + 3 = 6$. 7. Step 4: Add the fourth number: $6 + 4 = 10$. 8. Step 5: Add the fifth number: $10 + 5 = 15$. 9. So, the sum of the numbers from 1 to 5 is 15. 10. This method can be applied to any series or progression by adding each term explicitly and explaining the intermediate calculations clearly.