Question

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

Answer #1

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

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 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 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 if the series converges conditionally, converges
absolutely, or diverges.
/sum(n=1 to infinity) ((-1)^n(2n^2))/(n^2+4)
/sum(n=1 to infinity) sin(4n)/4^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...

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.

Test the series for convergence using the Alternating Series
Test: X∞ m=2 (−1)^m/ (m 2^m). If convergent, determine whether this
series converges absolutely or conditionally

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

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

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