Show that diverges if possible with Limit Comparison Test
Sum[1->inf] sin(1/n)
Sum[1->inf] sin(1/n)
-
Compare this series to the Harmonic series Σ(n = 1 to ∞) 1/n.
lim(n→∞) sin(1/n) / (1/n)
= lim(t→0+) sin(t)/t, with t = 1/n
= 1.
Since the Harmonic series diverges, so does the series in question by the Limit Comparison Test.
I hope this helps!
lim(n→∞) sin(1/n) / (1/n)
= lim(t→0+) sin(t)/t, with t = 1/n
= 1.
Since the Harmonic series diverges, so does the series in question by the Limit Comparison Test.
I hope this helps!