If possible show that diverges with Limit Comparison Test
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If possible show that diverges with Limit Comparison Test

[From: ] [author: ] [Date: 11-06-19] [Hit: ]
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Show that diverges if possible with Limit Comparison Test

Sum[1->inf] sin(1/n)

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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!
1
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