Just a written article about sums, it’s outside of class material, but it caught my eye when you guys asked. I’ll just write more about sums and summing in general.
When we have a sum, it’s a repeated adding of numbers, either complex, real, or any domain. The rules for adding something change, but we’ll stick to regular addition with real numbers.
The most basic sum is $a + b$ where a is real and b is real. All numbers are really sums. We can add more if we want! We can have $a + b + c$ too. If we keep going we have a long series of sums: $a + b + c + \dots + f$.
When the way we are summing has a general pattern as in a function’s image like $f(x) = 3x$, we can condense what we mean over
- a domain
- the form (function’s image)
and use what’s called sigma notation to express what we mean. For example, we can have
\[\sum_{x = 1}^{7} 3x\]to mean
\[3 + 6 + \dots + 21\]all without having to write out the entire series above. Time saving, right?
(all an illustration).