Provide an Appropriate Response $\sum _ { n = 1 } ^ { \infty } \frac { n } { 6 ^ { n - 1 } }$

question 175

Multiple Choice

Provide an appropriate response.
-Find the sum of the series $\sum _ { n = 1 } ^ { \infty } \frac { n } { 6 ^ { n - 1 } }$ by expressing $\frac { 1 } { 1 - x }$ as a geometric series, differentiating both sides of the resulting equation with respect to $x$ , and replacing $x$ by $\frac { 1 } { 6 }$ .

• A) \(\frac { 36 } { 49 }\)
• B) \(\frac { 36 } { 25 }\)
• C) \(\frac { 25 } { 36 }\)
• D) \(\frac { 49 } { 36 }\)

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Definitions:

Residual Value

Estimated value of an asset after all the allowable depreciation has been taken.

Useful Life

At the time an asset is acquired, an estimate is made of its usefulness in terms of years, output, and so forth.

Office Equipment

Assets like computers, printers, and furniture used in an office to perform business operations.

Units-Of-Production

A depreciation method that allocates cost based on the units produced by an asset over its useful life.