If We Add the First 100 Terms of the Alternating $1 - \frac { 1 } { 2 } + \frac { 1 } { 3 } - \frac { 1 } { 4 } + \frac { 1 } { 5 } - \cdots$

question 95

Multiple Choice

If we add the first 100 terms of the alternating series $1 - \frac { 1 } { 2 } + \frac { 1 } { 3 } - \frac { 1 } { 4 } + \frac { 1 } { 5 } - \cdots$ , how close can we determine the partial sum $S _ { 100 }$ to be to the sum $S$ of the series?

• A) \(s _ { 100 } > s \text {, with } s _ { 100 } - s < \frac { 1 } { 101 }\)
• B) \(s _ { 100 } > s , \text { with } s _ { 100 } - s < \frac { 1 } { e ^ { 100 } }\)
• C) \(s _ { 100 } > s \text {, with } s _ { 100 } - s < \frac { 1 } { 100 }\)
• D) \(s _ { 100 } < s , \text { with } s - s _ { 100 } < \frac { 1 } { e ^ { 101 } }\)
• E) \(s _ { 100 } > s , \text { with } s _ { 100 } - s < \frac { 1 } { e ^ { 101 } }\)
• F) \(s _ { 100 } < s \text {, with } s - s _ { 100 } < \frac { 1 } { 101 }\)
• G) \(s _ { 100 } < s \text {, with } s - s _ { 100 } < \frac { 1 } { 100 }\)
• H) \(s _ { 100 } < s , \text { with } s - s _ { 100 } < \frac { 1 } { e ^ { 100 } }\)

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