Question

Can anyone please answer this question​

Answer 1

Answer:

Both sides series are in GP. So apply GP summation formula,

$\frac{2 ln(a) }{1 - 2ln(a) } = 3 \times \frac{ ln(a) }{1 - ln(a) }$

let ln(a) = x then

$\frac{2x}{1 - 2x} = \frac{3x}{1 - x}$

$2x - 2 {x}^{2} = 3x - 6 {x}^{2}$

$4 {x}^{2} - x = 0$

$x(4x - 1) = 0$

$x = 0 \: or \: \frac{1}{4}$

so ln(a) = 0 then a = 1 (can't take)

i.e,

$ln(a) = \frac{1}{4}$

$a = e {}^{ \frac{1}{4} } = \sqrt[4]{e}$

option (D) correct.

mark BRAINLIEST if this is helpful to you. Thanks