By Calculating an Appropriate Number of Terms, Determine If the Series

question 193

Multiple Choice

By calculating an appropriate number of terms, determine if the series converges or diverges. If it converges, find the limit $L$ and the smallest integer $N$ such that $\left| a _ { n } - L \right| < 0.01$ for $n \geq N$ ; otherwise indicate divergence.
- $$a _ { n } = ( 1 + 0.153 / n ) ^ { n }$$

• A) \(\mathrm { L } \approx 1.1653 , \mathrm {~N} = 6\)
• B) \(\mathrm { L } \approx 1.153 , \mathrm {~N} = 6\)
• C) \(\mathrm { L } \approx 1.1653 , \mathrm {~N} = 2\)
• D) diverges

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Definitions:

Inputs

Resources such as labor, materials, and capital that are used in the production process to create goods or services.

Average Total Cost

The total cost divided by the quantity produced, calculating the per-unit cost of production.

Variable Cost

Charges that adjust in alignment with the volume of production or output levels.

Total Cost

The sum of fixed and variable costs incurred in the production of goods or services.