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

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To use the Nth term test on the infinite series ( \sum_{n=1}^{\infty} \sqrt{n}(2) ), follow these steps:

- Evaluate the Nth term of the series, which is ( \sqrt{n}(2) ).
- Determine the behavior of the Nth term as ( n ) approaches infinity.
- Apply the Nth term test, which states that if the limit of the Nth term as ( n ) approaches infinity does not equal zero, then the series diverges.
- If the limit is zero, the test is inconclusive, and other convergence tests may need to be applied.

Therefore, for the series ( \sum_{n=1}^{\infty} \sqrt{n}(2) ), calculate the limit of ( \sqrt{n}(2) ) as ( n ) approaches infinity. If the limit is not zero, the series diverges; if the limit is zero, further tests may be necessary to determine convergence.

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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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