Question

$\sqrt[3]{9 \sqrt[3]{9 \sqrt[ 3]{9} .... \infty } }$
please solve this​

Answer 1

Step-by-step explanation:

$\sqrt[3]{9 \sqrt[3]{9 \sqrt[3]{9}.... }}$

$= > \sqrt[3]{9 \sqrt[3]{9 \times {9}^{ \frac{1}{3}}.... } } \\ = > {9}^{ \frac{1}{3} } \times {9}^{ \frac{1}{9} } \times {9}^{ \frac{1}{27} } .... \\ = > {9}^{ \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + ... } \\ = > gp \: \: \: s = \frac{a}{1 - r} \\ = > a = \frac{1}{3} \\ = > r = \frac{ \frac{1}{9} }{ \frac{1}{3} } = \frac{1}{3} \\ = > s = \frac{ \frac{1}{3} }{1 - \frac{1}{3} } = \frac{ \frac{1}{3} }{ \frac{2}{3} } = \frac{1}{2} \\ = > {9}^{ \frac{1}{2} } \\ = > \sqrt{9} = 3$

Answer 2

$\huge \sf {\orange {\underline {\pink{\underline {♡A᭄ɴsᴡᴇʀ࿐ \ :- }}}}}$