Find the value of `9^(1/3), 9^(1/9). 9^(1/27)...up` to `oo.`

Options

A. 9
B. 3
C. `9^(1//3)`
D. 1

Answer

B

Explanation

The given expression `9^(1//3),9^(1//27)…oo`
Can be written as :
`9^((1)/(3)+(1)/(9)+(1)/(27)+…oo)=9^(((1)/(3))/(1-(1)/(3)))=9((1)/(3)//(2)/(3))=9^(1//2)=3`