Question

The sum \[ 1 + \frac{1+a}{2!} + \frac{1+a+a^2}{3!} + \cdots \] is equal to:

• A. \(e^a\)
• B. \(\dfrac{e^a-e}{a-1}\)
• C. \((a-1)e^a\)
• D. (a+1)eᵃ

Hint:

Break sums into known exponential series.

Answer 1

The Correct Option is B

Step 1: Write as difference of two exponential series and simplify to obtain (eᵃ-e)/(a-1).