On WolframAlpha I see that the sum of x+1 is given by

$\displaystyle \displaystyle\sum_{i=0}^{n} -\frac{1}{2}(n-2)(n+1) $

But if I want to start at i=1 this sum is no longer valid!! Was a surprise at first but i see now it makes sense, but then what is the way to adjust these partial sum formulas for starting at different numbers, or do I have to think of a totally new formula when i want to do something like this?

Thank you