A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Help please??
Find the sum of the infinite series 1/3 +4/9 + 16/27+ 64/81+...if it exists
anonymous
 one year ago
Help please?? Find the sum of the infinite series 1/3 +4/9 + 16/27+ 64/81+...if it exists

This Question is Closed

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Looks like \[\sum\dfrac{4^n}{3^{n+1}}\]

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1\[\cdots=\dfrac{1}{3}\sum\dfrac{4^n}{3^n} =\dfrac{1}{3}\sum\left(\dfrac{4}{3}\right)^n\]

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Now do you think this series exists?

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Well, this is geometric series, right?

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1And we have common ratio greater than 1.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah but I need to know what the sum of the series is

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1For any finite geometric series, formula is \[\sum_{i=1}^{n1} r^i = \dfrac{1r^n}{1r}\]Right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I think so, but what do put in to get the answer? Can you help walk me through the steps? I'm really confused.

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Do you know calculus?

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Really? ok well just take a look at \[\dfrac{1r^n}{1r}\] Since common ratio (r) is greater than 1, what would happen to it if n getting bigger and bigger? \(r^n\) would get bigger and bigger, right?

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1well, so when you "get" to infinity. You would have infinity in numerator.

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1So this series doesn't exist.

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Does that make sense?
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.