Estimate the Magnitude of the Error Involved in Using the Sum

question 337

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.
- $$\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } t ^ { n } } { n } , - 1 < t \leq 1$$

• A) \(\mid\) Error \(| < | \frac { t ^ { 5 } } { 5 } \mid\)
• B) \(\mid\) Error \(| < | t ^ { 5 } \mid\)
• C) \(\mid\) Error \(\mid < 0.20\)
• D) \(\mid\) Error \(| < | \frac { t ^ { 4 } } { 4 } \mid\)

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Definitions:

T Distribution

A distribution of probability applied to infer parameters of a population when the sample size is limited and the population's variance is not known.

Degrees Of Freedom

A statistical concept used to determine the number of independent pieces of information when estimating a parameter or fitting a model to data.

Normal Distribution

A bell-shaped frequency distribution curve, where most occurrences take place in the middle of the range and fewer occur on either side.

Endowment

A donation or funding given to an institution or individual to provide income for ongoing support.