Problem 221 (difficulty: 4/10)

Give an example of a positive sequence \(\displaystyle (a_n )\) for which \(\displaystyle \sqrt[n]{a_n}\to 1,\) but \(\displaystyle a_{n+1} /a_n \) does not tend to \(\displaystyle 1\). MegoEn E.g. merge \(\displaystyle b_n=1\) and \(\displaystyle c_n=n\).

Give me another random problem!