# What is the radius of convergence of the series #sum_(n=0)^oo(n*(x+2)^n)/3^(n+1)#?

Let

Using the Ratio Test

By eliminating common elements,

through multiplication by three

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The radius of convergence of the series is 1/3.

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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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