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GATE 2025 CE (CE1) – Question 3

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

The sum of the following infinite series is:

$$\frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \frac{1}{5!} + \cdots$$

  1. $\pi$
  2. $1 + e$
  3. $e - 1$
  4. $e$

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Correct answer: (C) $e - 1$

Explanation

The exponential series is $e = \frac{1}{0!} + \frac{1}{1!} + \frac{1}{2!} + \cdots = 1 + \frac{1}{1!} + \frac{1}{2!} + \cdots$. The given series is the same without the first term $\frac{1}{0!} = 1$, so its sum is $e - 1$.