# How do you find the limit of #s(n)=1/n^2[(n(n+1))/2]# as #n->oo#?

To find the limit of ( s(n) = \frac{1}{n^2}\left(\frac{n(n+1)}{2}\right) ) as ( n ) approaches infinity, you can simplify the expression and apply limit properties. The limit is ( \frac{1}{2} ).

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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.

- Lim n approaches infinity# 6/n((2n)/3 + (5n(n+1))/(2n) - (4n(n+1)(2n+1))/(6n^2))=#?
- Which of the following statements is true?
- How do you test the improper integral #int (x^2+2x-1)dx# from #[0,oo)# and evaluate if possible?
- How do you determine the convergence or divergence of #Sigma ((-1)^(n))/(ln(n+1))# from #[1,oo)#?
- Is the series #\sum_(n=1)^\inftyn^2/(n^3+1)# absolutely convergent, conditionally convergent or divergent?

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