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STD 11 - 8. sequence and series — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 8. sequence and series4 Marks
MCQ
$0.5737373...... = $
  • A
    $\frac{{284}}{{497}}$
  • B
    $\frac{{283}}{{495}}$
  • ✓
    $\frac{{568}}{{990}}$
  • D
    $\frac{{567}}{{990}}$
✓

Answer

Correct option: C.
$\frac{{568}}{{990}}$
c
(c) Given series $0.5737373……$

$= 0.5 + 0.073 + 0.00073$

$= 0.5 +$ $\frac{{73}}{{1000}} + \frac{{73}}{{100000}} + ....$

= $0.5 + 73\left[ {\frac{1}{{1000}} + \frac{1}{{100000}} + .....} \right]$

= $0.5 + 73\left[ {\frac{{1/1000}}{{1 - \frac{1}{{100}}}}} \right]$

= $0.5 + \frac{{73}}{{1000}}.\frac{{100}}{{99}} = \frac{5}{{10}} + \frac{{73}}{{990}}$

= $\frac{{495 + 73}}{{990}} = \frac{{568}}{{990}}$.

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