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

question 209

Multiple Choice

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

• A) - 150
• B) - 84
• C) - 216
• D) 132

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