Provide an Appropriate Response $\sum _ { n = 1 } ^ { \infty } \frac { n ^ { 2 } } { n ! }$

question 66

Multiple Choice

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

• A) 3(e - 1)
• B) e + 3
• C) 4e - 5
• D) 2e

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Definitions:

Genetically Predisposed

A condition where an individual has a higher likelihood of developing certain traits or diseases due to their genetic composition.

Epigenetics

Inquiry into the effects of gene expression modification on organisms, excluding alterations to the DNA sequence.

Gene Expression

The process by which the instructions in our DNA are converted into a functional product, such as a protein, playing a crucial role in biological functions and characteristics.

DNA Change

Alterations in the genetic material of an organism, which can occur naturally through mutation or be induced artificially, affecting traits and possibly resulting in genetic disorders or variations.