Question

Find the sum of the following geometric series, if it exists. Show work.
\[\frac{ 2 }{ 3 }+\frac{ 1 }{ 9 }+\frac{ 1 }{ 54 }...\]

Answer 1

use
\[\frac{a}{1-r}\] where \(a\) is the first term, i.e. \(a=\frac{2}{3}\)

Answer 2

I can't quite figure out r is the problem :(

Answer 3

of course you need to find \(r\) as well. do you know what it is ?

Answer 4

ok since the first term is \(a\) and the second term is \(ar\) that means you can always find \(r\) if it is not obvious, by dividing the second term by the first

Answer 5

Oh yea! I totally forgot about that :P

Answer 6

you could also ask yourself "what do i multiply \(\frac{2}{3}\) by to get \(\frac{1}{9}\) and come up with the answer \(\frac{1}{6}\) in your head more or less

Answer 7

but if not, you compute
\[\frac{1}{9}\div \frac{2}{3}=\frac{1}{9}\times \frac{3}{2}=...\]

Answer 8

Oh okay! :) I understand now. Thank you!

Answer 9

yw