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

We start with the geometric series

Then, assuming we can manipulate the infinite sum as if it were a finite sum, 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.

We start with the geometric series

Then, assuming we can manipulate the infinite sum as if it were a finite sum, we have