# How do you apply the ratio test to determine if #Sigma (1*3*5* * * (2n-1))/(n!)^2# from #n=[1,oo)# is convergent to divergent?

The series:

is convergent.

Write the series as:

We then evaluate the ratio for the series at hand:

so that:

which proves the series is convergent.

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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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