# How do you evaluate an infinite series?

See below

There are different types of series, to what use different methods of evaluating

For example a converging geometric series:

but there are other series what can be approached with tricks!

After consideration we can recognise this is the same as...

There are also other infinite series that you can remember, and may be able to prove, a like:

There are many others, where there insist one set way of computing infinite series, there are many!

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To evaluate an infinite series, you typically use various convergence tests to determine whether the series converges (has a finite sum) or diverges (has an infinite sum). Some common convergence tests include the comparison test, the ratio test, the root test, the integral test, and the alternating series test. Once you have determined that the series converges, you can use appropriate techniques such as geometric series summation, telescoping series summation, or other methods to find the sum of the series. If the series diverges, it means it does not have a finite sum.

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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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