Given the Series $\sum _ { m = 1 } ^ { \infty } \frac { 3 m } { 4 ^ { m } ( 3 m + 5 ) }$

question 92

Multiple Choice

Given the series $\sum _ { m = 1 } ^ { \infty } \frac { 3 m } { 4 ^ { m } ( 3 m + 5 ) }$ estimate the error in using the partial sum $s _ { 8 }$ by comparison with the series $\sum _ { m = 9 } ^ { \infty } \frac { 1 } { 4 ^ { m } }$ .

• A) \(R _ { 8 } \leq 2.6130051\)
• B) \(R _ { 8 } \geq 0.0000052\)
• C) \(R _ { 8 } \leq 0.0000051\)
• D) \(R _ { 8 } \geq 0.0000051\)
• E) \(R _ { 8 } \leq 0.000005\)

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Definitions:

Gross Profit

The financial metric that represents the difference between sales revenue and the cost of goods sold, before deducting overheads, payroll, taxation, and interest payments.

Profit Center

A branch or division of a company that is treated as a separate entity for the purpose of calculating its profitability.

Profit Center

A division or segment of a company that is directly responsible for generating its own revenue and profit through its activities.

Cost Center

A department or segment of a business that does not directly generate revenue but incurs costs, focusing instead on controlling expenses.