Value of {4^{1/3}}{.4^{1/9}}{.4^{1/27}}...........∞ is

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8. Sequences and Series

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The value of ${4^{1/3}}{.4^{1/9}}{.4^{1/27}}...........\infty $ is

A

$2$

B

$3$

C

$4$

D

$9$

Solution

(a) ${4^{1/3}}{.4^{1/9}}{.4^{1/27}}……\infty $

$\therefore $ $S = {4^{1/3 + 1/9 + 1/27}}……\infty $

$ \Rightarrow $ $S = {4^{\left( {\frac{{1/3}}{{1 – 1/3}}} \right)}} = {4^{\frac{{1/3}}{{2/3}}}}$$ $

$\Rightarrow $ $S = {4^{1/2}}$

$ \Rightarrow $ $S = 2$.

Standard 11

Mathematics

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