Use the Summation Properties to Evaluate the Series - $$\sum _ { i = 1 } ^ { 6 } \left( 2 i ^ { 2 } - i ^ { 3 } \right)$$

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

A) 623
B) $- 3108$
C) $- 259$
D) $- 1036$

Correct Answer:

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