A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
Is the serie \[\sum_{n=0}^{\infty} (1)^{n}\frac{ n+2 }{ 3^{n} }\]
convergent or divergent? Calculate is't value.
\[\lim_{n \rightarrow \infty} \left \left( \frac{ (1)^{n+1}(n+3) }{ 3^{n+1} } \right)\left( \frac{ 3^{n} }{ (1)^{n}(n+2) } \right) \right\]
\[\frac{ 1 }{ 3 } \lim_{n \rightarrow \infty} \left \frac{ n+3 }{n+2 } \right=\frac{ 1 }{ 3 }\]
\[\frac{ 1 }{ 3 } < 1; Convergent\]
But how do I calculate it's value?
anonymous
 3 years ago
Is the serie \[\sum_{n=0}^{\infty} (1)^{n}\frac{ n+2 }{ 3^{n} }\] convergent or divergent? Calculate is't value. \[\lim_{n \rightarrow \infty} \left \left( \frac{ (1)^{n+1}(n+3) }{ 3^{n+1} } \right)\left( \frac{ 3^{n} }{ (1)^{n}(n+2) } \right) \right\] \[\frac{ 1 }{ 3 } \lim_{n \rightarrow \infty} \left \frac{ n+3 }{n+2 } \right=\frac{ 1 }{ 3 }\] \[\frac{ 1 }{ 3 } < 1; Convergent\] But how do I calculate it's value?

This Question is Closed

phi
 3 years ago
Best ResponseYou've already chosen the best response.0I would try summing the negative terms and the positive terms

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Don't really know what you mean, should I expand the serie a couple of times then sum?

Zarkon
 3 years ago
Best ResponseYou've already chosen the best response.2\[\sum_{n=0}^{\infty} (1)^{n}\frac{ n+2 }{ 3^{n} }\] \[\sum_{n=0}^{\infty} n\left(\frac{1}{ 3 }\right)^n+2\sum_{n=0}^{\infty} \left(\frac{1}{ 3 }\right)^n\]

Zarkon
 3 years ago
Best ResponseYou've already chosen the best response.2\[2\sum_{n=0}^{\infty} \left(\frac{1}{ 3 }\right)^n\] is just a geometric sum...should be easy

Zarkon
 3 years ago
Best ResponseYou've already chosen the best response.2for \[\sum_{n=0}^{\infty} n\left(\frac{1}{ 3 }\right)^n\] write as \[\frac{1}{3}\sum_{n=0}^{\infty} n\left(\frac{1}{ 3 }\right)^{n1}\] then as \[\frac{1}{3}\sum_{n=0}^{\infty} n\left(x\right)^{n1}\] integrate this wrt x then compute the sum... then differentiate and plug in 1/3

Zarkon
 3 years ago
Best ResponseYou've already chosen the best response.2I get \[\frac{3}{16}+\frac{3}{2}=\frac{21}{16}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Your answer is correct according to my key, what's the metod you're using named? I think I need to study the concept a bit closer

Zarkon
 3 years ago
Best ResponseYou've already chosen the best response.2if a series converges uniformly then it can integrated or differentiated term by term

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I think I've found the section in my book now, don't get the concept yet but now I know where to start working on it. Thank you!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.