Question
Asked Sep 1, 2019
3 views
(-1)" n +n
2
30. The series
is
$3
n5n 1
A) Absolutely convergent
B) Conditionally convergent
C) Divergent
2
31. The series n
is
n+5n 1
A) Absolutely convergent
B) Conditionally convergent
C) Divergent
help_outline

Image Transcriptionclose

(-1)" n +n 2 30. The series is $3 n5n 1 A) Absolutely convergent B) Conditionally convergent C) Divergent 2 31. The series n is n+5n 1 A) Absolutely convergent B) Conditionally convergent C) Divergent

fullscreen
check_circle

Expert Answer

Step 1

Hey, since there are multiple questions posted, we will answer first question. If you want any specific question to be answered then please submit that question only or specify the question number in your message.

The given series can be written as follows.

help_outline

Image Transcriptionclose

(-1)n2 Σ (-1)n Σ n + n5n 1 n5n1 n5n 1 (-1)n 1 Σ Σ + n° 5n+1 1 n25 n 1 1 -Σ1)a +Σ , b_ b as 1 n25 n25 n n

fullscreen
Step 2

That is, the series is increasing and it contains only the positive terms.

help_outline

Image Transcriptionclose

Thus, it is bounded above by a convergent series n Hence, the series > b, is convergent and 27 n2 1 5 n+ 1 n 5n1 2 n n Σ-1)a,Σ_-) when a 1 a, and lima, ->0 5 n+-+ 2 n n So, the series is alternating with lima, ->0 and a,^ <a. ww.nnn is convergent Thus, the series n°5n 1 -

fullscreen
Step 3

Now for odd and even val...

help_outline

Image Transcriptionclose

(-1) n n n n If n is even, then 3 n 5n1 -nn n° 5n1 Ifn is odd, then (-1)n n 5n1 n 3 n 5n1 -nn So, for odd values of» -1)n - n5n1 n 11 3 n5n1

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Related Calculus Q&A

Find answers to questions asked by student like you
Show more Q&A
add