Question

does the infinite geometric series converge or diverge 2+6+ 18+ 54+ ...?

Answer 1

@skullpatrol help

Answer 2

@terenzreignz

Answer 3

Converge means they approach a certain number. Diverge means they don't.... usually because it goes to infinity.

Have a nice look at it... the terms keep going up and up, don't they?

Answer 4

yup

Answer 5

Well, what does your intuition say?
It keeps going up and up... is it ever going to approach a certain number?

Answer 6

so would it be diverge with no sum?

Answer 7

Yup.
An easier way to tell is if you have a geometric series, just divide the second term by the first.

If the quotient has an absolute value less than 1, then it converges
If the quotient has an absolute value greater than or equal to 1, then it definitely diverges.

Answer 8

thanks!

Answer 9

No problem ^^