# What is the interval of convergence of #sum_1^oo (-2)^n(n+1)(x-1)^n #?

Apply the test of ratios.

This provides

Condensed:

Assessing the maximum yields

leading to the disparity

Thus, the response is

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The interval of convergence of the series ∑ (-2)^n(n+1)(x-1)^n is (-1, 3), inclusive of -1 and exclusive of 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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