Question

plz anser it fast .. with solution

Answer 1

Heya

We use :
${6}^{m} \times {6}^{n} = {6}^{(m + n)}$

And hence,

${6}^{ \frac{1}{2} } \times {6}^{ \frac{2}{4} } \times {6}^{ \frac{3}{8} } \times ...$

$= {6}^{ \frac{1}{2} + \frac{2}{4} + \frac{3}{8} + \frac{4}{16} + ... }$
Hence, the sum of indices show an infinite AGP

Using a = ( 1 / 2 ) ; r = ( 1 / 2 ) ; d = ( 1 / 2 )

The sum equals :
$\frac{a}{1 - r} + \frac{dr}{( {1 - r})^{2} } = 1 + 1 = 2$

And hence, the product equals
${6}^{ \frac{1}{2} } \times {6}^{ \frac{2}{4} } \times {6}^{ \frac{3}{8} } \times ... = {6}^{2} = 36$

Hope this helps ^_^