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## Main Question or Discussion Point

So I am trying to derive a formula from one of the standard summation formulas except starting at a different index. So if I have the series..

[tex]\sum i = \frac{n(n+1)}{2}[/tex]

Where "i" runs from 1 to n. (I dont know how to put it in the code.) If I want to make the series start from zero, I would use another index equal to, "k=i-1" And now my upper limit will be "n-1" So now I can replace "i" in the sum with "k+1", Shouldn't the new formula for the partial sums be..

[tex]\sum k+1 = \frac{(n-1)(n)}{2} + (n-1)[/tex]

Problem is, it isnt. A simple test will prove this. Whats wrong?

[tex]\sum i = \frac{n(n+1)}{2}[/tex]

Where "i" runs from 1 to n. (I dont know how to put it in the code.) If I want to make the series start from zero, I would use another index equal to, "k=i-1" And now my upper limit will be "n-1" So now I can replace "i" in the sum with "k+1", Shouldn't the new formula for the partial sums be..

[tex]\sum k+1 = \frac{(n-1)(n)}{2} + (n-1)[/tex]

Problem is, it isnt. A simple test will prove this. Whats wrong?