# How does an infinite geometric series apply to being pushed on a swing?

If you wish to find the total horizontal distance traveled by you on a swing after a big initial push assuming that the amplitude of each swing decreases at a fixed rate. We can think of the total distance as the sum of a geometric series.

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An infinite geometric series can be used to model the motion of a swing. When you're pushed on a swing, your motion follows a repetitive pattern, much like the terms of a geometric series. As you swing back and forth, the distance you travel decreases with each swing, forming a geometric sequence. The total distance you travel over time can be represented by the sum of an infinite geometric series.

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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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