Question

**6. Let series {an} = 1/(n2 + 1) and series {bn} = 1/n2.
Use Limit Comparison Test to determine if each series is convergent
or divergent.**

**7. Use Ratio Test to determine if series {an}= (n +
2)/(2n + 7) where n is in interval [0, ∞]**

**is convergent or divergent. Note: if the test is
inconclusive, use n-th Term Test to answer the
question.**

**8. Use Root Test to determine if series {an} = nn/3(1 +
2n) where n is in interval [1, ∞] is convergent or
divergent.**

**9. Use Alternating Series Test to determine if series
{an} = (– 1)n–1/n is convergent or divergent.**

**10. Find Derivative and Integral of series {an}= xn/n = x +
x2/2 +x3/3 +…, where n is in interval [1, ∞].**

Answer #1

(1 point) The three series ∑An, ∑Bn, and ∑Cn have terms
An=1/n^8,Bn=1/n^5,Cn=1/n. Use the Limit Comparison Test to compare
the following series to any of the above series. For each of the
series below, you must enter two letters. The first is the letter
(A,B, or C) of the series above that it can be legally compared to
with the Limit Comparison Test. The second is C if the given series
converges, or D if it diverges. So for instance,...

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.

Are the series convergent or divergent. Use the direct
comparison test. If direct comparison test cannot be used, use the
limit comparison test. (a)∞∑n=1 2/(n^2−2) (b)∞∑n=2 1/((√n)−1 )

A) Use the Comparison Test to determine whether integral from 2
to infinity x/ sqrt(x^3 -1)dx is convergent or divergent.
B)Use the Comparison Test to determine whether the integral from
2 to infinity (x^2+x+2)/(x^4+x^2-1) dx is convergent or
divergent.

Use the RATIO test to determine whether the series is convergent
or divergent.
a) sigma from n=1 to infinity of (1/n!)
b) sigma from n=1 to infinity of (2n)!/(3n)
Use the ROOT test to determine whether the series converges or
diverges.
a) sigma from n=1 to infinity of
(tan-1(n))-n
b) sigma from n=1 to infinity of ((-2n)/(n+1))5n
For each series, use and state any appropriate tests to decide
if it converges or diverges. Be sure to verify all necessary...

We want to use comparison test in order to determine whether the
series is convergent or divergent. Which of the
following is correct?

Test the series for convergence or divergence.
∞
en
n2
n = 1
convergent or divergent

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...

Determine whether the given series is convergent or divergent.
Show you work and state the theorem/test you use.
Σ(-1)^n (sqrt(n))/(2n+3) n=1 and upper infinity

1.
Determine
whether the series is convergent or divergent.
a)
If
it is convergent, find its sum. (using only one of the THREE:
telescoping, geometric series, test for divergence)
summation from n=0 to infinity of
[2^(n-1)+(-1)^n]/[3^(n-1)]
b) Using ONLY
the
Integral Test.
summation from n=1 to infinity of
n/(e^(n/3))
Please give
detailed answer.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 20 minutes ago

asked 20 minutes ago

asked 32 minutes ago

asked 52 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago