Question

The value of $(1+\frac{1}{1\times 2}+\frac{1}{1\times 2\times 4}+\frac{1}{1\times 2\times 4\times 8}+\frac{1}{1\times 2\times 4\times 8\times 16})$ up to 4 places of decimal is

• A. $1.6416$
• B. $1.2937$
• C. $1.6414$
• D. $1.6415$

Answer 1

The correct option is A $1.6416$

Given exp. $=1+\frac{4\times 8\times 16+8\times 16+16+1}{1\times 2\times 4\times 8\times 16}$

$=1+\frac{512+128+16+1}{1024}$

$=1+\frac{657}{1024}$

$=1+0.6416=1.6416$