# If #a_n# converges and #a_n >b_n# for all n, does #b_n# converge?

See explanation below

We assume that we are talking about sequences (although, for infinite series, the reasoning is the quite similar)

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Yes, if (a_n) converges and (a_n > b_n) for all (n), then (b_n) also converges.

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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 determine the convergence or divergence of #Sigma 1/ncosnpi# from #[1,oo)#?
- How do you find #lim (sqrt(y+1)+sqrt(y-1))/y# as #y->oo# using l'Hospital's Rule?
- How do you determine if the series the converges conditionally, absolutely or diverges given #Sigma ((-1)^(n+1))/(n^1.5)# from #[1,oo)#?
- How do you use the Root Test on the series #sum_(n=1)^oo((n^2+1)/(2n^2+1))^(n)# ?
- How do you test the series #Sigma 1/(nlnn)# from n is #[2,oo)# for convergence?

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