Correct Answer - Option 1 : e
2
Concept used:
Expansion of ex
ex = \(1+\frac{x}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}+....\)
Calculation:
ex = \(1+\frac{x}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}+....\)
Put x = 2
∴ \(1+\frac{2}{1!}+\frac{4}{2!}+\frac{8}{3!}+\frac{16}{4!}+....\) = e2