Thank you for reporting, we will resolve it shortly
Q.
The value of $9^{1 / 3} \cdot 9^{1 / 9} \cdot 9^{1 / 27} \ldots \ldots$ upto $\infty$, is-
Sequences and Series
Solution:
We have to find value of $9^{1 / 3} \cdot 9^{1 / 9} \cdot 9^{1 / 27}$ $\infty=x$ (say)
We can see that powers are in G.P. and $|r|<1$
$\therefore x=9^{\frac{\frac{1}{3}}{1-\frac{1}{3}}}=9^{12}=3$