# How do you use the Nth term test on the infinite series #sum_(n=1)^ooln((2n+1)/(n+1))# ?

By the nth term test (Divergence Test), we can conclude that the posted series diverges.

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To use the Nth term test on the infinite series (\sum_{n=1}^\infty \ln\left(\frac{2n+1}{n+1}\right)), you need to examine the limit as (n) approaches infinity of the (n)th term of the series. This is done by taking the limit of the general term of the series, (\ln\left(\frac{2n+1}{n+1}\right)), as (n) tends to infinity. If this limit is not zero, then the series diverges. If the limit is zero, the test is inconclusive, and other tests may be needed to determine convergence or divergence.

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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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