Find the limit of 1/(n•cosn) as n tends to +∞.

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SUMMARY

The limit of the function 1/(n•cos(n)) as n approaches +∞ is not straightforward due to the behavior of cos(n), which oscillates between -1 and 1. While one participant incorrectly suggested that the limit is 0 by treating infinity as a number, the consensus indicates that the limit does not exist (DNE) because 1/cos(n) is unbounded. A mathematical approach to demonstrate this involves analyzing the oscillatory nature of cos(n) and its impact on the limit.

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Find the limit of 1/(n•cosn) as n tends to +∞.

I say the following:

1/[(∞)cos (∞)]

1/∞ = 0

The limit is 0.
 
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Harpazo said:
Find the limit of 1/(n•cosn) as n tends to +∞.

I say the following:

1/[(∞)cos (∞)]

1/∞ = 0

The limit is 0.

Not even close I'm afraid. You can NOT plug in infinity as though it's a number!

You are trying to use the fact that the product of a function that goes to 0 (in this case, 1/n) with a BOUNDED function has a limit of 0. But 1/cos(x) is not bounded.

I would be inclined to think that the limit does not exist.
 
Is there a more mathematical way to show the limit DNE?
 

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