Rewriting Sigma Notation (Index)

I don't see anything wrong with your sum. It's a bit quirky and unusual to start at $n = 2$ in this case, but it's not wrong, and it's not necessary to start at $1$. (As a reality check: why would we specify that we start at $1$ the times that we do, if it's a necessity? This isn't an airtight argument, mind you. Notation can be superfluous at times.)

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Summation

Algebra Precalculus

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