Find the value of the following expression upto four places of decimals.
$$\left[ {1 + \frac{1}{{1 \times 2}} + \frac{1}{{1 \times 2 \times 4}} + \frac{1}{{1 \times 2 \times 4 \times 8}} + \frac{1}{{1 \times 2 \times 4 \times 8 \times 16}}} \right]$$

A. 1.6414

B. 1.6415

C. 1.6416

D. 1.6428

Answer: Option C

Solution(By Examveda Team)

Given expression :
$$\eqalign{ & \left[ {1 + \frac{1}{{1 \times 2}} + \frac{1}{{1 \times 2 \times 4}} + \frac{1}{{1 \times 2 \times 4 \times 8}} + \frac{1}{{1 \times 2 \times 4 \times 8 \times 16}}} \right] \cr & = \frac{{2 \times 4 \times 8 \times 16 + 4 \times 8 \times 16 + 8 \times 16 + 16 + 1}}{{2 \times 4 \times 8 \times 16}} \cr & = \frac{{1024 + 512 + 128 + 16 + 1}}{{1024}} \cr & = \frac{{1681}}{{1024}} \cr & = 1.6416 \cr} $$