determine if the series below converges or diverges. for convergent series, find the sum of the series ∑_(k=0)^∞▒3(1/5) ^k

Question

anonymous · Answer

hi.  are you still there?

anonymous · Answer

if i am reading this right, it looks like a geometric series

turingtest · Answer

$$\sum_{k=0}^\infty3(\frac15)^k$$it looks like

turingtest · Answer

$$\sum_{k=0}^\infty a(n)^k=\frac a{1-n}~~~~~~~\forall n<1$$

nastech · Answer

I have no idea

anonymous · Answer

so the first term of your series is 3 because 3(1/5)^0=3

anonymous · Answer

1/5 is the common ratio

anonymous · Answer

the sum of the series is given by S=a/(1-r), a is the first term and r is the common ratio

anonymous · Answer

do this make sense to you?

turingtest · Answer

oh yeah, my formula is a bit off

nastech · Answer

i'm trying to put the pieces together

turingtest · Answer

oh no, it's right, nvm

anonymous · Answer

questions are ok here.

nastech · Answer

I get it now, thanks a lot. I'm actually supposed to create a matlab program to solve the question

anonymous · Answer

ahhh.  gotcha.  well, now you have the solution to check your work.   take care.  this geo series converges.  take care

nastech · Answer

you too take care and may God bless you