Question

Use the limit comparison test to determine whether the series Σ∞ n=1 (2^n)/(3+4^n) converges or diverges. Show your work. What series did you use for the comparison? How did you figure out the behavior (converge or diverge) of the series that you used for the comparison?

Answer #1

Use the ratio test to determine whether∑n=12∞n2+55n
converges or diverges.
(a) Find the ratio of successive terms. Write your
answer as a fully simplified fraction. For n≥12,
limn→∞∣∣∣an+1an∣∣∣=limn→∞
(b) Evaluate the limit in the previous part. Enter ∞
as infinity and −∞ as -infinity. If the limit does
not exist, enter DNE.
limn→∞∣∣∣an+1an∣∣∣ =
(c) By the ratio test, does the series converge,
diverge, or is the test inconclusive?

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

Figure out if the series Σ∞ n=1 (((n + 1)^426) / n! ) converges
or diverges. Explain answer completely.

Determine whether the following sequences converge or diverge.
If a sequence converges, find its limit. If a sequence diverges,
explain why.
(a) an = ((-1)nn)/
(n+sqrt(n))
(b) an = (sin(3n))/(1- sqrt(n))

Determine whether the following sequences converge or diverge.
If it converges, ﬁnd the limit. Must show work
1.)an = nsin(1/n)
2.)an = sin(n)
3).an =4^n /1 + 9^n
4).an = ln(n+1) − ln(n)

Determine whether the sequence converges or diverges. If it
converges, find the limit. (If an answer does not exist, enter
DNE.) a n = n 3 /n + 2

Determine whether the sequence converges or diverges. If it
converges, find the limit. (If an answer does not exist, enter
DNE.)
an = (4^n+1) /
9^n

Determine if the series converges or diverges (show your
work):
n! / nn

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

Determine whether the following series converges or
diverges:∞∑n=1 ln(1 +1/n).

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