Question

Show that sum sin(1/n)/n^p Converges Absolutely when p > 0.

Answer 1

sin(1/n) ~1/n if n>n0
so sum(sin(1/n)/n^p~1/n /n^p)= sum 1/n^(p+1)
then you have
when p+1>1 its converegent so p>0

Answer 2

could you please explain the middle part a little more