Use the Binomial Series to Find the Maclaurin Series for the Function

question 58

Multiple Choice

Use the binomial series to find the Maclaurin series for the function
$f ( x ) = \frac { 8 } { ( 1 + x ) ^ { 2 } }$

• A)\(\frac { 8 } { ( x + 1 ) ^ { 2 } } = 8 + 8 \sum _ { n = 0 } ^ { \infty } \frac { 1 \cdot 3 \cdot 5 \cdots ( 2 n - 1 ) x ^ { n } } { 2 ^ { n } n ! }\)
• B)\(\frac { 8 } { ( x + 1 ) ^ { 2 } } = 8 + 8 \sum _ { n = 1 } ^ { \infty } \frac { 1 \cdot 3 \cdot 5 \cdots ( 2 n - 1 ) x ^ { n } } { 2 ^ { n } n ! }\)
• C) \(\frac { 8 } { ( x + 1 ) ^ { 2 } } = 8 + 8 \sum _ { n = 0 } ^ { \infty } \frac { 1 \cdot 3 \cdot 5 \cdots ( 2 n - 1 ) x ^ { n } } { n ! }\)
• D) \(\frac { 8 } { ( x + 1 ) ^ { 2 } } = 8 \sum _ { n = 0 } ^ { \infty } \frac { 1 \cdot 3 \cdot 5 \cdots ( 2 n - 1 ) x ^ { n } } { 2 ^ { n } n ! }\)
• E)\(\frac { 8 } { ( x + 1 ) ^ { 2 } } = 8 \sum _ { n = 1 } ^ { \infty } \frac { ( 2 n - 1 ) x ^ { n } } { 2 ^ { n } }\)

---

Definitions:

Future Obligation

A commitment or responsibility to incur a cost or expenditure at a future date.

Vendor

An individual or business that supplies goods or services to another entity, often within a supply chain.

Products or Services

Refers to the goods that are manufactured and sold or the tasks that are performed by a business in exchange for money.

Individual

Refers to a single human being as separate from a group, class, or family.