PART II: Summation Notation Summation Formulas: ?_{i=1}^{n} i = n(n+1) / 2 ?_{i=1}^{n} i^2 = n(n+1)(2n+1) / 6 ?_{i=1}^{n} i^3 = n^2(n+1)^2 / 4 6. Use the properties of sigma notation and the summation formulas to evaluate the given sum. ?_{i=1}^{10} (i^2 - 2i + 3)
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First, we can rewrite the given summation as follows: $$\sum_{i=1}^{n} (2 - 2i + 3) = \sum_{i=1}^{n} (5 - 2i)$$ Now, we can split the summation into two separate summations: $$\sum_{i=1}^{n} (5 - 2i) = \sum_{i=1}^{n} 5 - \sum_{i=1}^{n} 2i$$ We can use the Show more…
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