Question

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

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

Answer 1

hey again,

you can see that a(n+1) = -a(n)/6
a(n+1) -> means the n+1 term

so now we can use the ratio test
lim |a(n+1)/an| as n-> inf = 1/6

1/6 is less than 1 so the series converges
if however we would get limit > 1 than we know that it diverges.

if you dont know about this ratio test tell me and we find another way to prove it :)