Provide an Appropriate Response $\mathrm { a } _ { \mathrm { n } }$

question 64

Multiple Choice

Provide an appropriate response.
-Which of the following statements is false?

• A) If \(\mathrm { a } _ { \mathrm { n } }\) and \(\mathrm { f } ( \mathrm { n } )\) satisfy the requirements of the Integral Test, and if \(\int _ { 1 } ^ { \infty } \mathrm { f } ( \mathrm { x } ) \mathrm { dx }\) converges, then \(\sum _ { \mathrm { n } = 1 } ^ { \infty } \mathrm { a } _ { \mathrm { n } } =\) \(\int _ { 1 } ^ { \infty } f ( x ) d x\)
• B) The integral test does not apply to divergent sequences.
• C) \(\sum _ { n = 1 } ^ { \infty } \frac { 1 } { { } _ { n } p }\) converges if \(p > 1\) and diverges if \(p \leq 1\).
• D) \(\sum _ { n = 2 } ^ { \infty } \frac { 1 } { n ( \ln n ) p }\) converges if \(p > 1\).

---

Definitions:

Collagen Production

The biological process involving the synthesis of collagen, a crucial protein for skin, bone, and connective tissue health and repair.

Dermis

The thick layer of living tissue below the epidermis, containing nerve endings, sweat glands, and blood vessels.

Neurological Deficits

Refers to impairments of the nervous system function, which can affect cognitive, physical, and emotional abilities.

Developmental Abnormalities

Atypical growth or psychological development patterns in children, potentially impacting learning and behavior.