# Does #a_n=(5^n)/(1+(6^n) #converge? If so what is the limit?

Yes, it converges to zero.

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To determine if the sequence ( a_n = \frac{5^n}{1 + 6^n} ) converges, we can analyze its behavior as ( n ) approaches infinity.

As ( n ) tends towards infinity, the term ( 6^n ) in the denominator becomes much larger than the term ( 5^n ) in the numerator. Therefore, the fraction ( \frac{5^n}{1 + 6^n} ) tends towards zero.

Thus, the sequence converges, and its limit as ( n ) approaches infinity 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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