Question

[ Part 1 ]

Determine the convergence or divergence, using the most appropriate test. State what test you are using and show your work.

1a) ∑ 1 / cos(2k·π)

1b) ∑ (−1)^k 1 / k+1

1c) ∑ ek^2 + 3k + 1 / π·k^12 + 5k + 3

Answer #1

Apply the Root Test to determine convergence or divergence, or
state that the Root Test is inconclusive.
from n=1 to infinity (3n-1/4n+3)^(2n)
Calculate lim n→∞ n cube root of the absolute value of an
What can you say about the series using the Root Test?
Determine whether the series is absolutely convergent,
conditionally convergent, or divergent.

Use the ratio test to determine convergence or divergence. If
the ratio test is inconclusive, use another method to determine
convergence or divergence.
∞
(−1)n(n!)2
/
(7n)!
n = 1
Its the series from 1 to infinity of
(-1)^n times (n!)^2 divided by (7n)!

Determine the convergence or divergence if each integral by
using a comparison function. Show work using the steps below:
A. Indicate the comparison function you are using.
B. Indicate if your comparison function is larger or smaller
than the original function.
C. Indicate if your comparison integral converges or diverges.
Explain why.
D. State if the original integral converges or diverges. If it
converges, you don’t need to give the value it converges to.
11. integral from 1 to infinity...

Determine the convergence/divergence of the following series
using the integral test:
a.) ∑= (1)/n(In(n))^2 (Upper limit of sigma is ∞ ,and the lower
limit of sigma is n=2)
b.) ∑ (n-4)/(n^2-2n+1) (Upper limit of sigma is ∞ and the lower
limit of the sigma is n=2
c.)∑ (n)/(n^2+1) (Upper limit of sigma ∞ and the lower limit
sigma is n=1)
d.) ∑ e^-n^2 (Upper limit of sigma ∞ and the lower limit sigma
is n=1)

Test the series for convergence or divergence. 1/ ln(2) − 1/
ln(3) + 1/ ln(4) − 1 /ln(5) + 1/ ln(6) −...

1. To test the series ∞∑k=1 1/5√k^3 for convergence, you can use
the P-test. (You could also use the Integral Test, as is the case
with all series of this type.) According to the P-test:
∞∑k=1 1/5√k^3 converges
the P-test does not apply to ∞∑k=1 1/5√k^3
∞∑k=1 1/5√k^3 diverges
Now compute s4, the partial sum consisting of the first 4 terms
of ∞∑k=1 1 /5√k^3:
s4=
2. Test the series below for convergence using the Ratio
Test.
∞∑n=1 n^5 /1.2^n...

1. Test the series below for convergence using the Root
Test.
∞∑n=1 (4n/10n+1)^n
The limit of the root test simplifies to lim n→∞ |f(n)| where
f(n)=
The limit is:
Based on this, the series
Diverges
Converges
2. We want to use the Alternating Series Test to determine if
the series:
∞∑k=4 (−1)^k+2 k^2/√k^5+3
converges or diverges.
We can conclude that:
The Alternating Series Test does not apply because the terms of
the series do not alternate.
The Alternating Series Test...

What statistical test is most appropriate if you want to
examine whether there is a difference in graduation rates
(percentages) between home schooling, public schools, and private
schools in your state of residence? Assume the data meets the
assumptions for a parametric test. (2 pts)
What statistical test would be most appropriate if you measured
religiosity (using an interval scale) every 5 years for a total of
20 years in the same participants (so, four data points per
person), but...

Test the series for convergence using the Alternating Series
Test: X∞ m=2 (−1)^m/ (m 2^m). If convergent, determine whether this
series converges absolutely or conditionally

1. Scores on the belief in UFO’s test are normally distributed
with m = 40 with a standard deviation of 3. Higher scores indicate
greater belief in UFO’s. A sample of 24 people is forced to watch
every episode of the X-Files TV show and then completes the test.
The sample has a mean score of 46. Does watching the X-Files
increase people’s belief in UFO’s? Use a = .01.
1a. The hypothesis test
should
be...
(highlight one) (1...

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