Question

If \( y = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots + \infty \), then

• A. \( x \)
• B. 1
• C. \( y \)
• D. None of these

Hint:

The Taylor series expansion for \( e^x \) is \( 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots \).

Answer 1

The Correct Option is C

Step 1: Recognize the Taylor series expansion.
The given series is the Taylor series expansion of \( e^x \), and thus \( y = e^x \).
Step 2: Conclusion.
Therefore, \( y = e^x \). Final Answer: \[ \boxed{y} \]