Provide an Appropriate Response $\sum _ { n = 1 } ^ { \infty } \frac { n ^ { 3 } } { n ! }$

question 81

Multiple Choice

Provide an appropriate response.
-Find the sum of the series $\sum _ { n = 1 } ^ { \infty } \frac { n ^ { 3 } } { n ! }$ .
[Hint: Write the series as $1 + 4 + \sum _ { n = 3 } ^ { \infty } \frac { n ^ { 3 } } { n ! } = 5 + \sum _ { n = 3 } ^ { \infty } \frac { n ( n - 1 ) ( n - 2 ) } { n ! } + 3 \sum _ { n = 3 } ^ { \infty } \frac { n ( n - 1 ) } { n ! } + \sum _ { n = 3 } ^ { \infty } \frac { n } { n ! }$ .]

• A) \(8 ( \mathrm { e } - 1 )\)
• B) \(3 \mathrm { e } + 5\)
• C) \(9 e - 11\)
• D) \(5 \mathrm { e }\)

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