# How do you use the direct comparison test for infinite series?

This test is very intuitive since all it is saying is that if the larger series comverges, then the smaller series also converges, and if the smaller series diverges, then the larger series diverges.

Let us look at some examples.

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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.

- Using the definition of convergence, how do you prove that the sequence #limit (sin n)/ (n) = 0# converges from n=1 to infinity?
- How do you determine the convergence or divergence of #Sigma ((-1)^(n+1))/(2n-1)# from #[1,oo)#?
- How do you determine whether the sequence #a_n=n!-10^n# converges, if so how do you find the limit?
- How do you know if the series #(1+n+n^2)/(sqrt(1+(n^2)+n^6))# converges or diverges for (n=1 , ∞) ?
- How do you use basic comparison test to determine whether the given series converges or diverges for #sum n/sqrt(n^2-1)# from n=2 to #n=oo#?

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