Estimate the Magnitude of the Error Involved in Using the Sum

question 398

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.
- $$\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } ( 0.3 ) ^ { 2 n + 1 } } { 2 n + 1 }$$

• A) \(\mid\) Error \(\mid < 1.61 \times 10 ^ { - 7 }\)
• B) \(\mid\) Error \(\mid < 2.19 \times 10 ^ { - 6 }\)
• C) \(\mid\) Error \(\mid < 1.77 \times 10 ^ { - 6 }\)
• D) \(\mid\) Error \(\mid < 4.43 \times 10 ^ { - 8 }\)

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