# How do you use sigma notation to write the sum for #1-1/2+1/4-1/8+...-1/128#?

For the basic pattern, we note this:

Next, the series is alternating from positive to negative. So we can this:

The sum is therefore:

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The given series can be represented using sigma notation as follows:

[ \sum_{n=0}^{6} (-1)^n \times \frac{1}{2^n} ]

This notation indicates the sum of the terms ( (-1)^n \times \frac{1}{2^n} ) from ( n = 0 ) to ( n = 6 ), which covers all terms of the given series up to ( -\frac{1}{128} ).

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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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