# Why does the integral test not apply to #Sigma (2+sinn)/n# from #[1,oo)#?

Because the condition only applies if

In fact, if we choose:

graph{(2+sinx)/x [-10, 10, -5, 5]}

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The integral test cannot be applied to ( \sum \frac{2+\sin(n)}{n} ) from ( n = 1 ) to ( \infty ) because the function ( f(n) = \frac{2+\sin(n)}{n} ) is not continuous, positive, and decreasing for all ( n \geq 1 ), which are the necessary conditions for the integral test to be applicable.

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The integral test cannot be directly applied to the series Σ(2 + sin(n))/n from [1, ∞) because the function (2 + sin(n))/n is not integrable over the interval [1, ∞). This means that the corresponding improper integral does not converge, and thus, the integral test cannot be used to determine the convergence of the 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.

- How do you test the series #Sigma n/sqrt(n^3+1)# from n is #[0,oo)# for convergence?
- How do you find the positive values of p for which #Sigma n/(1+n^2)^p# from #[2,oo)# converges?
- The series #sum_(n=1)^oo x^n/10^n # converges for #|x| lt beta#, find #beta#?
- How do you use the integral test to determine whether the following series converge of diverge #sum n/((n^2+1)^2)# from n=1 to infinity? Thanks for the help !!! I have no idea on how to do these questions?
- What is the radius of convergence by using the ratio test?

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