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Sequences and Series — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSSequences and Series1 Mark
MCQ
The value of $9^{\frac13}.9^{\frac19}.9^{\frac{1}{27}}\dots\text{to }\infty,$ is:
  • A
    1
  • B
    3
  • C
    9
  • D
    None of these.
✓

Answer

  1.  3

Solution:

$9^{\frac13}\times9^{\frac19}\times9^{\frac{1}{27}}\times\dots\infty$

$=9^{\big(\frac13+\frac19+\frac{1}{27}+\dots\infty\big)}$

Here, it is a G.P. with $\text{a}=\frac13$ and $\text{r}=\frac13.$

$\therefore9^{\Bigg(\frac{\frac{1}{3}}{1-\frac13}\Bigg)}$

$=9^{\big(\frac12\big)}=3$

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