This is not a question, i just wanted to post a detailed explanation of a property. this is a good thing to remember, and i had trouble understanding it at first, so i want to explain to others. i can now understand it and will explain in case someone is unsure. 1. ⁠the first sum is just 1 + 2 + 3 + + 10. which equals 55, times 2. which is 110. easy right? 2. ⁠the second sum is simply 2(1) + 2(2) + 2(3) + + 2(10). this is also equal to 110. 3. ⁠think of it like transferring the 2, from outside the first σ, to inside the second σ. so, logically you would be distributing the 2 to each term and then adding the up, instead of adding them up and then multiplying by 2. 4. ⁠if it , think if it like this: 2 ( 1 + 2 + 3 + + 10 ) = 2(1) + 2(2) + 2(3) + + 2(10). all you’re doing is distributing the 2 to each term. i hope this lets you understand the concept easier. i know this is not a very complicated idea, but i want to people understand the basics. it’s good to have a full understanding of the basic when you’re doing more complex math.