Show:
Geometric
P-Series/Oscillating series
Direct Comparison
Root/Ratio
Misc.
100
The geometric series is given by ∑ar^n = a + ar +ar^2 + ar^3 + ... converges with these values of r...
What is when the absolute value of r is less than one.
100
The values for which the p-series ∑1/np is convergent
What is when p>1
100
Let 0≤an≤bn for all n If ∑an converges, then ∑bn also converges True or False?
What is False?
100
limn→∞|an+1/an|=L The values of L in which the series ∑an is absolutely convergent.
What is when L<1?
100
When the Mississippi meets the Illinois River.
What is convergence?
200
The geometric series is given by ∑ar^n = a + ar +ar^2 + ar^3 + ... diverges with these values of r...
What is when the absolute value of r is greater than or equal to one.
200
The values for which the p-series ∑1/np is divergent.
What is when p<1
200
Let 0≤an≤bn for all n If ∑bn converges, then ∑an also converges True or False?
What is True?
200
limn→∞|an+1/an|=L The values of L in which the series ∑an is absolutely divergent.
What is when L>1
200
The confederate states wanted this.
What is a divergence.
300
The converging value of the geometric series ∑4(.5)^n.
What is 8.
300
As the number of terms approaches infinity, the P-series ∑1/(n^.07) does this.
What is divergent?
300
Let 0≤an≤bn for all n If ∑an diverges, then ∑bn also diverges True or False?
What is true?
300
limn→∞|an+1/an|=L The values of L in which the ratio test is inconclusive.
What is when L=1
300
Plato would let no man destitute of this series enter his halls.
What is geometric.
400
The converging value of the geometric series ∑(1/2)^n.
What is 2.
400
This is the p value of a series where the denominator is permanently square rooted.
What is p = 1/2?
400
Let 0≤an≤bn for all n If ∑bn diverges, then ∑an also diverges True or False?
What is false?
400
The series does this when the value for x^(n+1)/x^n is less than one when n approaches infinity.
What is converge.
400
Describes the motion of a hanging mass on a spring.
What is oscillating.
500
Write down the 8th term in the Geometric Progression 1, 3, 9, ... and the value of convergence as n approaches infinity?
The 8th term is 2187 and the series diverges.
500
A lonely cowboy plays an instrument that sounds like this series.
What is a harmonic series.
500
As the number of terms in the series ∑1/(3^n)+2 approaches infinity, the series does this.
What is converge?
500
The series does this when the value for x^(n+1)/x^n is greater than one when n approaches infinity.
What is diverge.
500
Spent 491 days as president. The 12th president of America. Same last name as a certain series.
Who is Zachary Taylor.