Thread: failure of ratio test examples

A) Give an example of a convergent sequence (Sn) of positive numbers such that lim (S(n+1) / Sn) = 1
B) Give an example of a divergent sequence (Tn) of positive numbers such that lim(T(n+1) / T(n) = 1

Originally Posted by learn18

A) Give an example of a convergent sequence (Sn) of positive numbers such that lim (S(n+1) / Sn) = 1

s_n=n

B) Give an example of a divergent sequence (Tn) of positive numbers such that lim(T(n+1) / T(n) = 1

s_n=1/n