The value of $\underset{\mathrm{x}\to \mathrm{\infty }}{\lim }\frac{2{\left(\mathrm{x}\right)}^{1/2}+3{\left(\mathrm{x}\right)}^{1/3}+4{\left(\mathrm{x}\right)}^{1/4}+.....+{\left(\mathrm{x}\right)}^{1/\mathrm{n}}}{{\left(2\mathrm{x}-3\right)}^{1/2}+{\left(2\mathrm{x}-3\right)}^{1/3}+....+{\left(2\mathrm{x}-3\right)}^{1/\mathrm{n}}}$ is

• Correct answer
  A

  $\sqrt{2}$
• B

  $2$
• C

  $\frac{1}{\sqrt{3}}$
• D

  $0$

Hence, the correct answer is option: 'A'.