Question

So lost.... Identify whether the series is a convergent or divergent geometric series and find the sum, if possible.

Answer 1

@bibby @jim_thompson5910 convergent or divergent help?

Answer 2

notice how the expression to the right of the sigma is of the form `a(r)^(n-1)`

where
a = 8
r = 5/6

Answer 3

Question: is |r| < 1 true?

Answer 4

it would be false, ?

Answer 5

r = 5/6 = 0.833

Answer 6

|r| < 1 is actually true since |0.833| < 1 is true

Answer 7

Now if |r| < 1 is true, then the infinite series converges to a fixed number

Answer 8

Which happens to be
\[\Large S = \frac{a}{1-r}\]

Answer 9

I'm sorry I made an assumption without even doing the work, my apologies lol. duh. plug in the numbers and then answer your question

Answer 10

So I'll continue and get one of these answers :
This is a convergent geometric series. The sum is 48.
This is a divergent geometric series. The sum is 48.
This is a convergent geometric series. The sum cannot be found.
This is a divergent geometric series. The sum cannot be found.

Answer 11

It would be, A from what I've read?

Answer 12

yeah because

S = a/(1-r)
S = 8/(1-5/6)
S = 48

Answer 13

Thank you so much, helped being walked through a little bit. Have a good night!