Question

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

Answer #1

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

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

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.

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.

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...

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 )

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

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

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

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