# Does #a_n=(8000n)/(.0001n^2) #converge? If so what is the limit?

The sequence converges to 0.

Alternatively, you can use L'Hospital's rule to simplify, though this takes a bit more work. It will yield the same result. By this rule, if:

Take the derivative of the numerator and denominator:

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To determine if the sequence ( a_n = \frac{8000n}{0.0001n^2} ) converges, we can analyze its behavior as ( n ) approaches infinity.

First, simplify the expression:

( a_n = \frac{8000n}{0.0001n^2} = \frac{8000}{0.0001n} )

As ( n ) approaches infinity, the denominator ( 0.0001n ) becomes infinitely large, and the sequence tends towards zero.

Therefore, the sequence converges, and its limit is ( 0 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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