Summation Notation Formula

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Is there some sort of mental formula I could develop that would allow me to form a summation notation equation to express any form of addition? I'm trying to figure out how to express [A..B] in summation notation. If A is 1 and B is 10, then it equals 1+2+3+4+5+6+7+8+9+10. You basically take the factorial of the second variable and subtract it from the factorial of the first variable, but that formula doesn't work when you introduce a third variable, like [A..B..C].