Step 1: Eliminate the options
Lanthanide series: stable except Pm, so it cannot be the answer.
p block and transition elements: most members are stable.
Step 2: Remaining option
The 5f series, actinoids, has no stable isotope for any of its members.
Step 3: Conclusion
Hence the actinoids are the series in which all elements are radioactive.
Final Answer:
Only the actinoids have all members radioactive.
\[ \boxed{\text{(B) }\text{Actinoids}} \]