# What is the interval of convergence of #sum(2^n(x-3)^n)/(sqrt(n+3))#?

Test of ratios:

which implies either:

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The interval of convergence for the given series is ( |x - 3| < 1 ), or equivalently, ( 2 < x < 4 ).

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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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