Question

Does the following infinite geometric series diverge or converge? Explain.

1/5 + 1/25 + 1/125 + 1/625

A) It diverges; it has a sum.
B) It converges; it has a sum.
C) It diverges; it does not have a sum.
D) It converges; it does not have a sum.

I am pretty sure that it is divergent. I am only confused by the part of it having a sum. How do I know when a geometric series has a sum.

Answer 1

Notice that is simply a geometric series, where
a = 1/5, r = 1/5

since Sum(all terms) = a/(1-r)
= (1/5)/(4/5)
= 1/4 , it clearly converges

What made you think it diverges?
What have you studied about diverging and converging series?

( simply adding the first 4 already gives us .2496 )

Answer 2

I found this formula for it. -1>r>1
Sorry, I meant converge. I went back and looked at the video. They said converge.