Thread: ratio test divergence proof

A) Give an example of an unbounded sequence that does not diverge to
(+ infinity) or to ( - infinity)

B) Let (Sn) be a sequence of positive terms such that the sequences of ratios ( (S(n+1)/Sn)) converges to L. Prove that if L>1, then Lim Sn = + infinity

Originally Posted by luckyc1423

A) Give an example of an unbounded sequence that does not diverge to
(+ infinity) or to ( - infinity)

What about,
a_n=(-1)^n*n

B) Let (Sn) be a sequence of positive terms such that the sequences of ratios ( (S(n+1)/Sn)) converges to L. Prove that if L>1, then Lim Sn = + infinity

Here.