Question

The value of $9^{1/3}\cdot 9^{1/9}\cdot 9^{1/27}\dots \dots$ upto $\infty$, is-

• A. 1
• B. 3
• C. 9
• D. 27

Answer 1

Answer: (B)

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 $|r|<1$
$\therefore x=9^{\frac{\frac{1}{3}}{1-\frac{1}{3}}}=9^{12}=3$