All Flashcards
What is the general form of a p-series?
What is the formula for the harmonic series?
How do you determine convergence/divergence of ?
Identify p = 2. Since 2 > 1, the series converges.
How do you determine convergence/divergence of ?
Rewrite as . Identify p = 1/2. Since 1/2 < 1, the series diverges.
How do you determine convergence/divergence of ?
Simplify to . Identify p = 1. Since p=1, the series diverges (Harmonic Series).
Determine convergence/divergence of
Identify p = 0.75. Since 0.75 < 1, the series diverges.
Determine convergence/divergence of
Rewrite as . Identify p = 4. Since 4 > 1, the series converges.
Determine convergence/divergence of
Simplify to . Identify p = 3/2. Since 3/2 > 1, the series converges.
Determine convergence/divergence of
Rewrite as . Identify p = 3. Since 3 > 1, the series converges.
Define a p-series.
A series of the form , where p is a constant.
Define a harmonic series.
A p-series where p = 1, represented as .
What does it mean for a series to converge?
The sum of the infinite terms approaches a finite value.
What does it mean for a series to diverge?
The sum of the infinite terms does not approach a finite value; it tends to infinity or oscillates.