Determine whether the series
Summation from n equals 0 to infinity e Superscript negative 5
n∑n=0∞e^−5n...
Determine whether the series
Summation from n equals 0 to infinity e Superscript negative 5
n∑n=0∞e^−5n
converges or diverges. If it converges, find its sum.
Select the correct choice below and, if necessary, fill in the
answer box within your choice.
A.The series converges because
ModifyingBelow lim With n right arrow infinitylimn→∞
e Superscript negative 5 ne−5nequals=0.
The sum of the series is
nothing.
(Type an exact answer.)
B.The series diverges because it is a geometric series with
StartAbsoluteValue r...
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...
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
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...
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...
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?
(1 point) The three series ∑An, ∑Bn, and ∑Cn have terms
An=1/n^8,Bn=1/n^5,Cn=1/n. Use the Limit Comparison...
(1 point) The three series ∑An, ∑Bn, and ∑Cn have terms
An=1/n^8,Bn=1/n^5,Cn=1/n. Use the Limit Comparison Test to compare
the following series to any of the above series. For each of the
series below, you must enter two letters. The first is the letter
(A,B, or C) of the series above that it can be legally compared to
with the Limit Comparison Test. The second is C if the given series
converges, or D if it diverges. So for instance,...
1. To test the series ∞∑k=1 1/5√k^3 for convergence, you can use
the P-test. (You could...
1. To test the series ∞∑k=1 1/5√k^3 for convergence, you can use
the P-test. (You could also use the Integral Test, as is the case
with all series of this type.) According to the P-test:
∞∑k=1 1/5√k^3 converges
the P-test does not apply to ∞∑k=1 1/5√k^3
∞∑k=1 1/5√k^3 diverges
Now compute s4, the partial sum consisting of the first 4 terms
of ∞∑k=1 1 /5√k^3:
s4=
2. Test the series below for convergence using the Ratio
Test.
∞∑n=1 n^5 /1.2^n...