Question

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?

Answer #1

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 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

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?

Consider the series ∑n=1 ∞ an
where
an=(5n+5)^(9n+1)/
12^n
In this problem you must attempt to use the Ratio Test to decide
whether the series converges.
Compute
L= lim n→∞
∣∣∣an+1/an∣∣
Enter the numerical value of the limit L if it converges, INF if
the limit for L diverges to infinity, MINF if it diverges to
negative infinity, or DIV if it diverges but not to infinity or
negative infinity.
L=
Which of the following statements is true?
A. The...

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

Determine whether each of the following series converges or not.
(Name the test you use. You do not have to evaluate the sums of
these series). Please write as big and neatly as possible
in your answer, demonstrating all steps.
a) Sum infinity n = 1 of square root n/n^3+1
b) Sum infinity n = 2 of 1/nln(n)

Determine whether each of the following series converges or not.
(Name the test you use. You do not have to evaluate the sums of
these series). Please write as large and neatly as possible
in your answer for ease of reading, demonstrating all steps. Thank
you.
a) Sum infinity n = 1 of square root n/n^3+1
b) Sum infinity n = 2 of 1/nln(n)

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