1 + x + x²/2 – x⁴/8 – x⁵/15 + … =

Correct option is C

​$$\text{To recognize the series, consider the \textbf{Maclaurin (Taylor) expansion} of the exponential of a function:} \\[6pt]e^{f(x)} = 1 + f(x) + \frac{f(x)^2}{2!} + \frac{f(x)^3}{3!} + \cdots \\[10pt]\text{Now let's check the \textbf{Maclaurin expansion} of } e^{\sin x}. \\[12pt]\textbf{Step-by-Step Expansion:} \\[6pt]\text{We know:} \\\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \cdots \\[6pt]\text{Then:} \\e^{\sin x} = 1 + \sin x + \frac{\sin^2 x}{2!} + \frac{\sin^3 x}{3!} + \cdots \\[10pt]\text{Now compute a few terms of the expansion:} \\[6pt]\textbf{First few terms:} \\[4pt]\circ \ \sin x = x - \frac{x^3}{6} + \frac{x^5}{120} + \cdots \\[4pt]\circ \ \text{So:} \\e^{\sin x} = 1 + x + \frac{x^2}{2} - \frac{x^4}{8} - \frac{x^5}{15} + \cdots$$​​