Question

The value of the product
$6^{\frac{1}{2}}\times 6^{\frac{1}{4}}\times 6^{\frac{1}{8}}\times 6^{\frac{1}{16}}\times ..$ up to infinite terms is

• A. $6$
• B. $36$
• C. $216$
• D. $512$

Answer 1

The correct option is A $6$

$6^{\frac{1}{2}}\times 6^{\frac{1}{4}}\times 6^{\frac{1}{8}}........$

$=6^{(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}.......)}$

$=6^{\left(\frac{\frac{1}{2}}{1-\frac{1}{2}}\right)}$

$=6^1=6$

Hence, the answer is $6$.