Infinite Sequences and Series (BC Only)
For what values of does the infinite series converge according to the p-Series Test?
When .
Only when .
When .
For all positive values of .
For the series what is the p-value of the series?
2
The series is not a p-series
Which of the following sums is representative of the harmonic series?
If the series is convergent for , what is the impact on convergence if is replaced with in this p-series?
The series may or may not converge depending on whether .
The convergence of the series remains unaffected by this change in .
The series will always converge since it initially converged for .
The series will always diverge regardless of the value of .
Which series definitely diverges based on its form?
Harmonic series, .
P-series where .
Geometric series where ratio r satisfies .
Alternating harmonic series, .
What is the relationship between a harmonic series and a p-series?
A p-series is a type of harmonic series
A harmonic series is a p-series with p-value of 1
There is no relation between a p-series and a harmonic series
All p-series are also harmonic series, but not all harmonic series are p-series
Given a p-series , for which value of will it be guaranteed to converge?

How are we doing?
Give us your feedback and let us know how we can improve
How does replacing every term in the harmonic sequence with their respective natural logarithms affect its convergence?
The transformed sequence still maintains conditional convergence similar to original alternating sign property's influence.
It causes divergence as natural logarithms grow slower than linear functions which alters summability negatively.
It has no significant impact as both sequences tend towards infinity and have diminishing terms contributing less over time.
It creates absolute convergence due to slow growth rate of natural logarithms compared to harmonic terms.
What conclusion can be drawn about the convergence of the series using alternating series tests?
It diverges because its nth term does not approach zero.
It converges because terms decrease in absolute value.
It converges by comparison to a known convergent series.
Convergence cannot be determined without further analysis.
If the series is known to converge, what does this imply about the behavior of its sequence of partial sums?
The terms in the series approach zero as approaches infinity.
The sequence of partial sums diverges to infinity.
The sequence of partial sums oscillates between two bounds.
The sequence of partial sums approaches a finite limit.