Question

If *a**n* converges and *b**n*
diverges, can anything be said about their term-by-term
*a**n**+**b**n* ? Give reasons
for your answer

Answer #1

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 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 if the series converges or diverges. Justify your
answer by stating the test used and the conditions of the test.
\sum _{n=0}^{\infty } [100+\sqrt{n}]/[4n^2-6n+1]

*answer in detail, give example
Suppose a given alternating series diverges. Can it converge
absolutely? (yes or no?) Justify 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?

Conception Question about bounded. If you avoid to answer my
question and only said based on the definition, I will give you
thumb down.
Q1, When we say that the sequence is bounded, it means that it
is bounded above and below. However, why the
definition only says that there exists x<=M,
obviously, this is bounded above. should we also have the little m?
such as m<=x<=M ?
Q2. When we say the sequence bounded by M, does that mean...

What are the limits to U.S. long-term economic growth? Is there
anything that our government can do to address these limits, or
would it be a bad idea to try? Minimum of 250 words

It is given that ∑an (an >0) is convergent
a) What can be said about the convergence of
∑an.an+1
b) Is the series ∑an1+an
convergent? Show your work!

What, if anything, can be considered ironic about the setting of
Shirley Jackson’s “the lottery”?

What can be said about a space curve with constant
acceleration?

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