The value of the series $2/3! + 4/5! + 6/7! + \cdots$ is
- A. 2e^{-2}
- B. e^{-2}
- C. e^{-1}
- D. 2e^{-1}
✅ Correct Answer: e^{-1}
Explanation
Rewrite the series $= (3-1)/3! + (5-1)/5! + (7-1)/7! + \cdots$ $= 1/2! - 1/3! + 1/4! - 1/5! + \cdots$ $= 1 + (-1)/1! + 1/2! - 1/3! + 1/4! - \cdots$ $= e^{-1}$
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