Question

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)!/(3^{n})

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 conditions for the tests you use, state your conclusion, and clearly show all work.

a)sigma from n=1 to infinity of e^{n}/n^{2}

b) sigma from n=1 to infinity of n/sqrt(n^{5}+n+1)

Answer #1

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

Determine whether the given series are absolutely convergent,
conditionally convergent or divergent: a.) sigma ∞to n=0 (−3)n\(2n
+ 1)!
b.) sigma ∞ ton=1 (2n)!\(n!)2

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

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.

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.

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

abs convergent, condit. convergent or divergent?
A. infinity sigma k=2 (1/(k(lnk)^3)
B. infinity sigma k=2 ((-9^(2n))/(n^2*8^n)

Determine whether the following series is absolutely convergent,
conditionally convergent, or divergent. State the name of the test
you apply, and show that the series satisfies all hypotheses of the
test. Show All Work.

Determine whether the series is convergent or divergent. If it
is convergent, find its sum.
(a) ∑_(n=1)^∞ (e2/2π)n
(b) ∑_(n=1)^∞ 〖[(-0.2)〗n+(0.6)n-1]〗
(c) ∑_(k=0)^∞ (√2)-k

how do I show if the series sigma(n=1 to infinity)
cos(npi/3)/(n!) is divergent, conditionally convergent, or
absolutely convergent?

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