Question

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

Answer #1

Determine if each of the following series converges or diverges
showing all the work including all the tests used. Find the sum if
the series converges.
a. Σ (n=1 to infinity) (3^n+1/ 7^n)
b. Σ (n=0 to infinity) e^n/e^n + n

Determine whether the limit converges or diverges, if it
converges, find the limit.
an = (1+(4/n))^n

18. Give an example.
1. A series whose first term is 20 and whose sum converges to
30.
2. A series that converges conditionally and whose denominator
is 7k^7.
3. A series that diverges but is inconclusive when applying the
Ratio Test.

Determine whether the sequence a_n = (3^n + 4^n)^(1/n) diverges
or converges

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

1) Determine if the sequence converges or Diverges. If it
converges find the limit.
an=n2*(e-n)

Prove that a sequence (un such that n>=1)
absolutely converges if the limit as n approaches infinity of
n2un=L>0

Determine whether the improper integral from 5 to infinity
3/square root x dx converges or diverges, and find the value if it
converges.
Select the correct choice below and fill in any answer boxes
within your choice.
A. The value of the integral
B.The integral diverges.

Determine whether the sequence converges or diverges. If it
converges, find the limit. (If an answer does not exist, enter
DNE.)
an = 4 − (0.7)n
lim n→∞ an =
please box answer

Suppose X∞ n=0 cnxn converges when x = −4
and diverges when x = 6. State if the following series are
convergent or divergent, or if there is not information to
determine convergence or divergence.
(a) X∞ n=0 cn3n
(b) X∞ n=0 cn5n
(c) X∞ n=0 cn7n

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