The GATE Grind

GATE 2014 EC (EC4) – Question 11

Engineering Mathematics · Calculus · 1 mark · Multiple choice

To what does $\sum_{n=0}^{\infty}1/n!$ converge?

  1. $2\ln2$
  2. $\sqrt2$
  3. $2$
  4. $e$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (D) $e$

Explanation

The exponential Taylor series is eˣ=Σₙ₌₀∞xⁿ/n!. Setting x=1givesΣ1/n!=**e,D**. The n=0term contributes1because0!=1; omitting it would give e−1instead.