hi, i have a chart, at 0.25, the value is 1/64

at 0.5, the value is 1/16

at 0.75 the value is 9/64

at 1, the value is 1

how can this information be written in summation notation?

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- Dec 18th 2007, 10:49 AM #1

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- Dec 18th 2007, 11:01 AM #2

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- Dec 18th 2007, 11:02 AM #3

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- Dec 18th 2007, 11:13 AM #4

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- Dec 18th 2007, 11:15 AM #5

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well basically, i was to pick points on a graph and then check their heights at that point and then find the area of a rectangle formed with the width and the height. these values represent the x values and then the area, and my assignment is to rewrite that info in summation notation.

- Dec 18th 2007, 11:28 AM #6

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I have no clue how to go about that problem. Are the areas being summed? If so, I get the impression that you are approximating the area under a curve using rectangles (presumably to eventually derive the integral from a Reimann sum). I think that is way off base though. Sorry.

- Dec 18th 2007, 08:35 PM #7

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I suspect this assignment has been given in preparation for learning how to integrate and that you are supposed to use the sum of the areas of these rectangles as an approximation for the area under the curve.

Summation notation is not exceedingly useful if you do not have an equation for the curve. You could however refer to your heights as $\displaystyle y_1$,$\displaystyle y_2$ etc, in which case you could make use of summation notation for the sum of the areas as follows (using your first set of data).

$\displaystyle \sum_{i=1}^{4}\frac {1}{4} y_i$