Question

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)!/(3^{n})

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 conditions for the tests you use, state your conclusion, and clearly show all work.

a)sigma from n=1 to infinity of e^{n}/n^{2}

b) sigma from n=1 to infinity of n/sqrt(n^{5}+n+1)

Answer #1

Determine whether the given series is convergent or divergent.
Show you work and state the theorem/test you use.
Σ(-1)^n (sqrt(n))/(2n+3) n=1 and upper infinity

Determine whether the given series is convergent or divergent.
Show you work and state the theorem/test you use.
Σ (2)/(sqrt(n)+2) n=1 and upper infinity

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.

Determine whether the series is convergent or divergent. If it
is convergent, find its sum.
(a) ∑_(n=1)^∞ (e2/2π)n
(b) ∑_(n=1)^∞ 〖[(-0.2)〗n+(0.6)n-1]〗
(c) ∑_(k=0)^∞ (√2)-k

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 or divergence.
∞
en
n2
n = 1
convergent or divergent

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...

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...

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 series
∞
∑
n=1
(e^n+1+ (−1)^n+1)/(π^n)
converges or diverges. If it is convergent, find its
sum.

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