Question

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.

Answer #1

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

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

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...

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

c.) Determine whether the seriesX∞ k=1 k(k^4 + 2k)/(3k 2 − 7k^5)
is convergent or divergent. If it is convergent, find the sum.
d.) Determine whether the series X∞ n=1 n^2/(n^3 + 1) is
convergent or divergent.

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

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

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

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