# How to find the sum of this series?

##
The following series satisfies the hypothesis of the alternating series test

#1/(1*9) - 1/(2*9^2)+1/(3*9^3)-1/(4*9^4)+...#

Approximate the sum of the series to two decimal place accuracy.

The following series satisfies the hypothesis of the alternating series test

Approximate the sum of the series to two decimal place accuracy.

We have

Let's solve the general case instead, as that's going to be easier to understand.

Let's separate the positive powers and negative powers, respectively :

Now, we know that

Back to our original sum :

#1/(1*color(red)9) - 1/(2*color(red)9^2) + 1/(3*color(red)9^3) -...
=#

In order to approximate it, we have to use a formula :

The inequality above helps us deduce that, consequently ,

Finally,

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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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