How the hell do you know if this sequence converges or diverges
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How the hell do you know if this sequence converges or diverges

[From: ] [author: ] [Date: 11-11-24] [Hit: ]
......
tan((4npi)/(4+16n))

I tried taking the limit as n approaches infinity but how in the world do I find the limit for that function?

-
lim 4nπ/(4 + 16n) = π/4
n->∞

Moreover, 0 ≤ 4nπ/(4 + 16n) < π/4 for all n. So

lim tan(4πn/(4 + 16n) = tan(π/4) = 1.
n->∞
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