Question

Find the value of \(1+\frac{2}{1!}+\frac{4}{2!}+\frac{8}{3!}+\frac{16}{4!}+....\)
1. e²
2. e
3. 1
4. log 1

Answer 1

Correct Answer - Option 1 : e²

Concept used:

Expansion of e^x 

e^x = \(1+\frac{x}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}+....\)

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