How do you use the integral test to determine if #1/(sqrt1(sqrt1+1))+1/(sqrt2(sqrt2+1))+1/(sqrt3(sqrt3+1))+...1/(sqrtn(sqrtn+1))+...# is convergent or divergent?
The series is divergent. See the explanation below.
This is the series:
Before starting with the integral test, we need to see that a couple conditions are met first.
Then:
This is just as valid a method as the integral test, but quicker.
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To use the integral test to determine the convergence or divergence of the series :
- Check if the series terms are positive, which they are.
- Verify that the series terms are decreasing, which they are.
- Integrate the function from to .
- Determine if the integral converges or diverges.
If the integral converges, then the series also converges. If the integral diverges, then the series also diverges.
By integrating the function and evaluating the integral, you can determine the convergence or divergence of the given series.
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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.
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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