Use the Summation Properties to Evaluate the Series - $$\sum _ { i = 1 } ^ { 3 } \left( - 3 i ^ { 2 } + 4 i - 5 \right)$$

question 203

Multiple Choice

Use the summation properties to evaluate the series. The following rules may be needed: $$\sum _ { i = 1 } ^ { n } i = \frac { n ( n + 1 ) } { 2 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 2 } = \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 3 } = \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 } .$$
- $$\sum _ { i = 1 } ^ { 3 } \left( - 3 i ^ { 2 } + 4 i - 5 \right)$$

• A) - 23
• B) - 3
• C) 23
• D) - 33

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