Question

Consider the series ∑*n*=1 ∞ *a**n*
where

*a**n*=(5*n*+5)^(9*n*+1)/
12^*n*

In this problem you must attempt to use the Ratio Test to decide
whether the series converges.

Compute

*L*= lim *n*→∞
∣∣∣*a**n*+1/*a**n*∣∣

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 Ratio Test says that the series converges
absolutely.

**B**. The Ratio Test says that the series
diverges.

**C**. The Ratio Test says that the series converges
conditionally.

**D**. The Ratio Test is inconclusive, but the series
converges absolutely by another test or tests.

**E**. The Ratio Test is inconclusive, but the series
diverges by another test or tests.

**F**. The Ratio Test is inconclusive, but the series
converges conditionally by another test or tests.

Enter the letter for your choice here: ?

Answer #1

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

Test the series for convergence or divergence.
∞
(−1)n
8n − 5
9n + 5
n = 1
Step 1
To decide whether
∞
(−1)n
8n − 5
9n + 5
n = 1
converges, we must find lim n → ∞
8n − 5
9n + 5
.
The highest power of n in the fraction is
1
1
.
Step 2
Dividing numerator and denominator by n gives us lim n
→ ∞
8n − 5
9n +...

Find a general term (as a function of the variable n) for the
sequence{?1,?2,?3,?4,…}={45,1625,64125,256625,…}{a1,a2,a3,a4,…}={45,1625,64125,256625,…}.
Find a general term (as a function of the variable n) for the
sequence {?1,?2,?3,?4,…}={4/5,16/25,64/125,256/625,…}
an=
Determine whether the sequence is divergent or convergent. If
it is convergent, evaluate its limit.
(If it diverges to infinity, state your answer as inf . If it
diverges to negative infinity, state your answer as -inf . If it
diverges without being infinity or negative infinity, state your
answer...

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?

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...

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