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

question 51

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:

Short-Term Debt

Loans or borrowings that are due for repayment within a short timeframe, typically within one year, used for immediate financing needs.

Retained Earnings

The portion of net income not distributed as dividends to shareholders, but retained by the company for reinvestment.

MACRS 3-Year Class

A category under the Modified Accelerated Cost Recovery System (MACRS) for depreciating certain types of business property over three years.

Amortized

Amortization is the process of spreading out a loan into a series of fixed payments over time, covering both principal and interest.