Question

Determine whether the sequence converges or diverges. If it converges, give the limit.

108, -18, 3, - (1/2),...

Answer 1

Well, it seems, it is a geometric sequence. Taking,
\[a_0=108\]And finding the ratio r,
\[r=-18/(108)=-1/6\]Then
\[a_n=108(-1/6)^n\]As this is an alternate sequence I would say it cannot converge.

Answer 2

I have to correct myself. This sequence is convergent, because the even and odd terms tends to 0.

Answer 3

So, the limit is 0.

Answer 4

It Converges; 0 ?

Answer 5

Yes, exactly.

Answer 6

Thank You. :)

Answer 7

You're welcome.