Question

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.

Answer #1

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 each series is absolutely convergent,
conditionally convergent, or divergent. X∞ n=1 (−1)n−1
(n /n 3/2 + 1)

Classify the series as absolutely convergent, conditionally
convergent, or divergent:
∞
∑ ((−1)^?) (1)/√(?(?+1))
?=1

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

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

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

Identify the following series as convergent or divergent. State
which test you are using, and show your work. E (n^2)/(2n)!

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.

Identify the following series as convergent or divergent. State
which test you are using, and show your work. E
(9^n)/((-2)^(n+1))n

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...

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