# How do you test for convergence of #Sigma (3n-7)/(10n+9)# from #n=[0,oo)#?

By putting an limit in front.

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To test the convergence of the series Σ(3n-7)/(10n+9) from n=0 to infinity, you can use the limit comparison test. Let's compare it with the series Σ1/n.

First, find the limit of the ratio of the two series as n approaches infinity:

lim (3n-7)/(10n+9) / (1/n) = lim (3n-7)/(10n+9) * n = lim (3n^2 - 7n) / (10n + 9) = lim (3 - 7/n) / (10 + 9/n) = 3/10

Since the limit is a finite nonzero number, and 1/n is a p-series with p=1, which is known to converge, by the limit comparison test, the given series 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.

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