A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Find the sum of the infinite geometric series, if it exists. 4 - 1 +1/4 -1/16 + . . . A. - 1 B. 3 C. 16/5 D. does not exist

  • This Question is Open
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1433468481845:dw|

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    We have to find the common ratio since they told us this a geometric sequence. A common ratio (r) is basically the number divided by the preceding one. If we look at the sequence, we see that the common ration is -1/4 because: \[(-1) / (4) = -1/4\] \[(1/4)/(-1)= -1/4 \] \[(-1/16)/(1/4)= -1/4\] Now, there is a formula for finding the sum of an infinite geometric sequence. Basically, there is only one condition: \[\Large \left| r \right|<1\] Or in other words \[\Large -1<r<1\] r= -1/4 so it will work. The formula is \[\Large Sum~of~a~geometric~sequence~(S_\infty)=\] \[\Large \frac{ a_1 }{ 1-r }\] Where \[\Large a_1=first~term\] \[\Large r=~common~ratio\] Now plug in a_1= 4 and r= -1//4 in and tell me what you get

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Everywhere I said sequence, I meant series*

  4. courtneygraley009
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Use this math calculator to solve this geometric series. http://www.acalculator.com/quadratic-equation-calculator-formula-solver.html

  5. Error1603
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    b

  6. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.