# Using the definition of convergence, how do you prove that the sequence #lim 1/(6n^2+1)=0# converges?

and so:

which proves the limit.

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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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- 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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