If lim n → ∞ 0.000003 a n = L {\textstyle \lim _{n\to \infty }0.000003a_{n}=L} for some value L {\displaystyle L} in the real line, then lim n → ∞ a n = 1000000 L / 3 {\textstyle \lim _{n\to \infty }a_{n}=1000000L/3} , so its contrapositive implies that if { a n } {\textstyle \{a_{n}\}} diverges then so must { 0.000003 a n } {\textstyle \{0.000003a_{n}\}} .
Answer: The statement is true . {\displaystyle \color {blue}{\text{true}}.}
