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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
$1 + \frac{3}{2} + \frac{5}{{{2^2}}} + \frac{7}{{{2^3}}} + ......\,\infty \,$ is equal to
  • A
    $3$
  • B
    $6$
  • C
    $9$
  • ✓
    $12$
✓

Answer

Correct option: D.
$12$
d
(d) It is an arithmetico-geometric series

${S_\infty } = \frac{a}{{1 - r}} + \frac{{dr}}{{{{(1 - r)}^2}}}$$ = \frac{1}{{1 - \frac{1}{2}}} + \frac{2}{{{{\left( {1 - \frac{1}{2}} \right)}^2}}}$$ = \frac{2}{{\frac{1}{2}}} + \frac{2}{{\frac{1}{4}}}$

$ = 4 + 8 = 12$.

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