Question

Consider the infinite series: (2/5) + (2*6) /(5*8) + (2*6*10) / (5*8*11) + (2*6*10*14) / (5*8*11*14) +........

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

Answer #1

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Determine whether each series is absolutely convergent,
conditionally convergent, or divergent. X∞ n=1 (−1)n−1
(n /n 3/2 + 1)

determine whether the alternating series ∑ (1 to ^ infinity)
(-1)^(n+1) 3^n / (n +1)! is absolutely convergent, conditionally
convergent or divergent.

Determine whether the given series are absolutely convergent,
conditionally convergent or divergent: a.) sigma ∞to n=0 (−3)n\(2n
+ 1)!
b.) sigma ∞ ton=1 (2n)!\(n!)2

Determine whether the following series is absolutely convergent,
conditionally convergent, or divergent. State the name of the test
you apply, and show that the series satisfies all hypotheses of the
test. Show All Work.

Test the series for convergence using the Alternating Series
Test: X∞ m=2 (−1)^m/ (m 2^m). If convergent, determine whether this
series converges absolutely or conditionally

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 the Root Test to determine convergence or divergence, or
state that the Root Test is inconclusive.
from n=1 to infinity (3n-1/4n+3)^(2n)
Calculate lim n→∞ n cube root of the absolute value of an
What can you say about the series using the Root Test?
Determine whether the series is absolutely convergent,
conditionally convergent, or divergent.

c.) Determine whether the seriesX∞ k=1 k(k^4 + 2k)/(3k 2 − 7k^5)
is convergent or divergent. If it is convergent, find the sum.
d.) Determine whether the series X∞ n=1 n^2/(n^3 + 1) is
convergent or divergent.

Given the alternating series:
sigma(2 to infinity): (-1)^n / ln n
Determine if the series converge
absolutely. (Use the fact
that: ln n <
n)
Determine if the series converge
conditionally.
(Estimate the sum of the infinite series using the
first 4 terms in the series and estimate the
error.
How many terms should we use to approximate the sum of
the infinite series in question, if we want the error to be less
than 0.5?

1. Consider the following time series data.
t
1
2
3
4
5
Yt
6
11
9
14
15
a. Develop the linear trend equation for this
time series (to 1 decimal).
Tt = (___) + (___) t
b. What is the forecast for t=6 (to 1
decimal)?
(___)
2. Consider the following time series data.
t
1
2
3
4
5
Yt
7
11
9
14
16
a. Develop the linear trend equation for this
time series (to 1...

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