Question

What is the meaning of convergent and divergent series? Explain your answer with example.

Answer #1

Classify the series as absolutely convergent, conditionally
convergent, or divergent:
∞
∑ ((−1)^?) (1)/√(?(?+1))
?=1

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.

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

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.

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

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

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

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

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

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

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