Question

Are the series convergent or divergent. Use the direct comparison test. If direct comparison test cannot be used, use the limit comparison test. (a)∞∑n=1 2/(n^2−2) (b)∞∑n=2 1/((√n)−1 )

Answer #1

We want to use comparison test in order to determine whether the
series is convergent or divergent. Which of the
following is correct?

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...

Make two non-zero series, one convergent and one divergent, that
we can use ratio test to conclude convergence and divergence,
respectively. The series cannot be geometric series.

1.
Determine
whether the series is convergent or divergent.
a)
If
it is convergent, find its sum. (using only one of the THREE:
telescoping, geometric series, test for divergence)
summation from n=0 to infinity of
[2^(n-1)+(-1)^n]/[3^(n-1)]
b) Using ONLY
the
Integral Test.
summation from n=1 to infinity of
n/(e^(n/3))
Please give
detailed answer.

Test the series for convergence or divergence.
∞
en
n2
n = 1
convergent or divergent

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

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)!/(3n)
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...

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

Identify the following series as convergent or divergent. State
which test you are using, and show your work. E
(9^n)/((-2)^(n+1))n

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

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