Question

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

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 alternating series ∑ (1 to ^ infinity)
(-1)^(n+1) 3^n / (n +1)! is absolutely convergent, conditionally
convergent or divergent.

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.

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)

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...

3. Let ∑an be a conditionally convergent series. Prove that
there exists a rearrangement ∑a_f(n) diverging to positive
infinity

Given the alternating series:
sigma(2 to infinity): (-1)^n / ln n
Determine if the series converge
absolutely. (Use the fact
that: ln n <
n)
Determine if the series converge
conditionally.
(Estimate the sum of the infinite series using the
first 4 terms in the series and estimate the
error.
How many terms should we use to approximate the sum of
the infinite series in question, if we want the error to be less
than 0.5?

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.

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