Using Borel-Cantelli to find limsup
Hint: If $(a_n)$ is a sequence of real numbers with $\lim \sup {|a_1+a_2+\cdots+a_n|}/n <\infty$ then $\lim \sup \frac {|a_n|} n <\infty$.
Using Borel-Cantelli to find limsup
Hint: If $(a_n)$ is a sequence of real numbers with $\lim \sup {|a_1+a_2+\cdots+a_n|}/n <\infty$ then $\lim \sup \frac {|a_n|} n <\infty$.