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 \(p > 1\).

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