# How do you find the n-th partial sum of an infinite series?

To find the n-th partial sum of an infinite series, you add up the first n terms of the series. Mathematically, this can be represented as:

[ S_n = a_1 + a_2 + a_3 + \ldots + a_n ]

Where ( S_n ) is the n-th partial sum and ( a_1, a_2, a_3, \ldots ) are the terms of the series.

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The partial sum is

by regrouping,

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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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