Determine whether the sequence converges or diverges. If it converges, give the limit.

60, -10, five divided by three, negative five divided by eighteen, ...

Question

Determine whether the sequence converges or diverges. If it converges, give the limit. 

60, -10, five divided by three, negative five divided by eighteen, ...

agent0smith · Answer

You need to find the common ratio first - divide any term by the term right before it (use the first two terms since it's easiest to)

anonymous · Answer

i got -1/6

agent0smith · Answer

so the common ratio, r = -1/6. 

If |r| < 1, the sequence converges. Is |-1/6| < 1?

anonymous · Answer

The fraction looks like it will eventually be a small over large, so 0. That implies it should converge. The rest is finding the limit. Have you tried this reference for the topic? http://tutorial.math.lamar.edu/Classes/CalcII/ConvergenceOfSeries.aspx

anonymous · Answer

wait what

agent0smith · Answer

so the common ratio, r = -1/6. 

If |r| < 1, the sequence converges. Is |-1/6| < 1?

anonymous · Answer

1/6

agent0smith · Answer

Yes, but is |-1/6| < 1 ?

anonymous · Answer

no

agent0smith · Answer

Why not? 1/6 = 0.16 recurring.

anonymous · Answer

oh pellet yes because its aqbsolute value

agent0smith · Answer

Not because it's absolute value, but because 1/6th is less than 1.

agent0smith · Answer

So it converges, since |r| < 1

agent0smith · Answer

"If it converges, give the limit. " I guess they just want what the terms approach... I don't know if they want the value of the sum or not.

anonymous · Answer

Diverges

 Converges; 11100

 Converges; 72

 Converges; 0

agent0smith · Answer

The value of the sum: $$\Large \frac{ a_1 }{ 1-r }$$first term a1 and r, plug them in

anonymous · Answer

how do i get r though

agent0smith · Answer

You just found r :P

agent0smith · Answer

In the second post you gave it

anonymous · Answer

i got all -10

agent0smith · Answer

First term was 60, r=-1/6$$\Large \frac{ 60 }{ 1-\left( -  \frac{ 1 }{ 6 }\right)}$$

anonymous · Answer

60.1666

agent0smith · Answer

Use a calculator, and make sure you use brackets.

agent0smith · Answer

http://www.wolframalpha.com/input/?i=+%5Cfrac%7B+60+%7D%7B+1-%5Cleft%28+-++%5Cfrac%7B+1+%7D%7B+6+%7D%5Cright%29%7D Looks like none of the answer choices are correct for the sum, so maybe they just meant the limit of the terms The terms will approach zero, so Converges; 0

anonymous · Answer

Oh man this was confusing lolol