Problem 192 (difficulty: 3/10)

 *  [a)] \(\displaystyle a_n\to 1\). Does it imply that \(\displaystyle a_n^n\to 1\)?
 *  [b)] \(\displaystyle a_n>0, a_n\to 0\). Does it imply that \(\displaystyle \sqrt[n]{a_n}\to 0\)?
 *  [c)] \(\displaystyle a_n>0, a_n\to a>0\). Does it imply that \(\displaystyle \sqrt[n]{a_n}\to 1\)?
 *  [d)] \(\displaystyle c_nd_n\to 0\). Does it imply that \(\displaystyle c_n\to 0\) or \(\displaystyle d_n\to 0\)?

Give me another random problem!