Question

Determine whether the series

∞

∑

n=1

(e^n+1+ (−1)^n+1)/(π^n)

converges or diverges. If it is convergent, find its

sum.

Answer #1

Determine whether the following series converges or
diverges:∞∑n=1 ln(1 +1/n).

Determine whether the limit converges or diverges, if it
converges, find the limit.
an = (1+(4/n))^n

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

Determine if each of the following series converges or diverges
showing all the work including all the tests used. Find the sum if
the series converges.
a. Σ (n=1 to infinity) (3^n+1/ 7^n)
b. Σ (n=0 to infinity) e^n/e^n + n

1) Determine if the sequence converges or Diverges. If it
converges find the limit.
an=n2*(e-n)

Determine where series converges or diverges:
∑(-1)n(n!)2/(2n)!

Determine whether the series
Summation from n equals 0 to infinity e Superscript negative 5
n∑n=0∞e^−5n
converges or diverges. If it converges, find its sum.
Select the correct choice below and, if necessary, fill in the
answer box within your choice.
A.The series converges because
ModifyingBelow lim With n right arrow infinitylimn→∞
e Superscript negative 5 ne−5nequals=0.
The sum of the series is
nothing.
(Type an exact answer.)
B.The series diverges because it is a geometric series with
StartAbsoluteValue r...

State whether the given series converges or diverges, and
why.
#21 sum 1/n^5, n=1 to infinity
#22 sum 1/5^n, n=0 to infinity
#23 sum 6^n / 5^n, n=0 to infinity
#24 sum n^-4, n=1 to infinity
#25 sum sqrt(n), n=1 to infinity

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.

Use the limit comparison test to determine whether the series Σ∞
n=1 (2^n)/(3+4^n) converges or diverges. Show your work. What
series did you use for the comparison? How did you figure out the
behavior (converge or diverge) of the series that you used for the
comparison?

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