Solution
= Solution
Take \b[$\boxed{a_n=(-1)^n}$]. Then $|a_n/n|=1/n\to0$, but $a_{n+1}-a_n=-2(-1)^n$ alternates between $2$ and $-2$. Thus convergence of the scaled <sequence> does not imply convergence of its successive differences.
= Solution
Take \b[$\boxed{a_n=(-1)^n}$]. Then $|a_n/n|=1/n\to0$, but $a_{n+1}-a_n=-2(-1)^n$ alternates between $2$ and $-2$. Thus convergence of the scaled <sequence> does not imply convergence of its successive differences.