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Geometric Series and Sums

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Please see the attached Microsoft Word document.
Thanks for your expertise.

Part A Find a specific geometric that sums up to 30.
Part B Can you find a specific geometric series that sums to -30 ?
Part C Can you find a specific geometric series summing up to - ?
Part D Determine precisely which real numbers can be sums of a geometric series.

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Solution Summary

This provides examples of working with geometric series and sums.

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Part A Find a specific geometric that sums up to 30.
Solution
There are two possibilities to determine sum of two geometric series.
Suppose, if we take first term a=2, number of terms 4 and r = 2 then sum

In case of infinite series then
...

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