Question

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.

Answer #1

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...

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

Say the ratio test and give an example of an alternating series
that converges absolutely by the ratio test.

6. Let series {an} = 1/(n2 + 1) and series {bn} = 1/n2.
Use Limit Comparison Test to determine if each series is convergent
or divergent.
7. Use Ratio Test to determine if series {an}= (n +
2)/(2n + 7) where n is in interval [0, ∞]
is convergent or divergent. Note: if the test is
inconclusive, use n-th Term Test to answer the
question.
8. Use Root Test to determine if series {an} = nn/3(1 +
2n) where n...

Apply term-wise integration to the expansion 1/(1 − x) = ∑∞ n=0
x n = 1 + x + x^2 + x^3 + ... to prove that for −1 < x < 1, −
ln(1 − x) = ∑∞ n=0 (x^n+1)/(n + 1) = x + x^2/2 − x^3/3 + x^4/4 +
... You should find a constant that appears when you integrate. (b)
Study convergence of this new series at the end points of the
interval (−1, 1). (c)...

1) Give an example of a type I error.
2.
Give an example of a type II error.
3.
What type of t-test would you use when the same group is tested
twice at different time points?

Example 1: Future Value (FV) of a Present Single
Sum
Your client
has $500,000 in an IRA and has asked you to estimate
its value
when the client reaches retirement age in 8 years, assuming
a 6% return each year.
Example 2: Future Value (FV) of a present single Sum
with
Multiple Interest Rates
Same facts
as Example 1 except the client would like to adjust the
asset
allocation of the investments over time, evolving from a
more
aggressive strategy...

1. Consider the following optimization problem. Find two
positive numbers x and y whose sum is 50 and whose product is
maximal. Which of the following is the objective function?
A. xy=50
B. f(x,y)=xy
C. x+y=50
D. f(x,y)=x+y
2. Consider the same optimization problem. Find two positive
numbers x and y whose sum is 50 and whose product is maximal. Which
of the following is the constraint equation?
A. xy=50
B. f(x,y)=xy
C. x+y=50
D. f(x,y)=x+y
3. Consider the same...

Exhibit 17-1
Below you are given the first five values of a quarterly time
series. The multiplicative model is appropriate and a four-quarter
moving average will be used.
Year
Quarter
Time Series Value Yt
1
1
36
2
24
3
16
2
4
20
1
44
Refer to Exhibit 17-1. An estimate of the trend component times
the cyclical component (T2Ct) for Quarter 3
of Year 1, when a four-quarter moving average is used, is
Group of answer choices
24...

1. Give an example of using a weighted mean. how might it be a
better average than another measure of center like the mean?
2. Fill in the second column of the table
with any numbers you want.
This column will represent number of students
who had a certain score on a test.
Score
N (weight)
60
70
80
90
Calculate Weighted Mean for the score on this test.
Discussion C: The mean and the median are two types
of measures...

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