Obtain the following formula without attempting to justify the steps used in the process.

Starting with the formula for the sum of a geometric series and differentiating both sides (without justifying that we can do this) we have

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Stumbling Robot

A Fraction of a Dot
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Without justification, establish the given formula

Obtain the following formula without attempting to justify the steps used in the process.

Starting with the formula for the sum of a geometric series and differentiating both sides (without justifying that we can do this) we have