Question

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 EndAbsoluteValuergreater than or equals≥1.

C.The series diverges because

ModifyingBelow lim With n right arrow infinitylimn→∞e Superscript negative 5 ne−5nnot equals≠0

or fails to exist.

D.The series converges because it is a geometric series with

StartAbsoluteValue r EndAbsoluteValuerless than<1.

The sum of the series is

nothing.

(Type an exact answer.)

E.The series converges because

ModifyingBelow lim With k right arrow infinitylimk→∞Summation from n equals 0 to k∑n=0k e Superscript negative 5 ne−5n

fails to exist.

Answer #1

Please thumbs up if it was helpful will be glad to know;)

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...

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

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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