Question

Does the following infinite geometric series diverge or converge? Explain.
7 + 21 + 63 + 189 + . .

Answer 1

An infinite geometric series converges if its common ratio r satisfies –1 < r < 1. Otherwise it diverges.

Answer 2

It converges; it has a sum.
It converges; it does not have a sum.
It diverges; it has a sum.
It diverges; it does not have a sum.

Answer 3

that means....r should be decimal

Answer 4

it converges and has a sum
diverges and has no sum

Answer 5

I can only pick one :o

Answer 6

Hint:
\(common~ratio\) means a given term divided by the previous term.
@PrincessKhiayla

Answer 7

converges and have a sum

Answer 8

Thank you @mathmate @lalithavasanth

Answer 9

\[a _{n}\rightarrow \infty ~as~n \rightarrow \infty \]
hence it does not converge.

Answer 10

I'm confused :o

Answer 11

\[a _{n}must \rightarrow 0~as~ n \rightarrow \]

Answer 12

\[n \rightarrow \infty \]

Answer 13

sorry i am leaving.

Answer 14

So it does converge?

Answer 15

@PrincessKhiayla
First, you recognize that this is a geometric series since each term divided by the previous is a constant. This ratio is called the common ratio.
Can you tell me the value of the common ratio r?

Answer 16

It doesn't say @mathmate

Answer 17

No it doesn't.
You have to calculated it according to what I explained.

Answer 18

Oh okay