Estimate the Magnitude of the Error Involved in Using the Sum

question 422

Multiple Choice

Estimate the magnitude of the error involved in using the sum of the first four terms to approximate the sum of the entire series.
- $$\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } \frac { 1 } { 6 ^ { n } }$$

• A) \(\mid\) Error \(\mid < 1.29 \times 10 ^ { - 4 }\)
• B) \(\mid\) Error \(\mid < 7.72 \times 10 ^ { - 4 }\)
• C) \(\mid\) Error \(\mid < \frac { 1 } { n }\)
• D) \(\mid\) Error \(\mid < 2.14 \times 10 ^ { - 5 }\)

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Definitions:

Sales-Type Lease

A lease agreement where the lessor recognizes profit or loss upfront due to the difference between the fair value of the asset and its carrying amount.

Initial Direct Costs

Expenses directly associated with obtaining or originating a financing lease, which are often deferred and amortized over the lease term.

Interest Rate Implicit

The interest rate implicit in a lease is the rate of interest that, when applied to the cash flows of the lease, causes the present value of these flows to equal the fair value of the leased asset at the inception of the lease.

Prepaid Asset

Expenses paid in advance by a company, such as insurance or rent, that are recorded as assets until they are utilized.