If sum of series 1 + frac{2}{x} + frac{4}{{{x^2}}} + frac{8}{{{x^3}}} + ....∞ is a finite number,

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8. Sequences and Series

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If the sum of the series $1 + \frac{2}{x} + \frac{4}{{{x^2}}} + \frac{8}{{{x^3}}} + ....\infty $ is a finite number, then

A

$x > 2$

B

$x > - 2$

C

$x > \frac{1}{2}$

D

None of these

Solution

(a) Common ratio $(r) = \frac{2}{x}$

For sum to be finite $r < 1$

$ \Rightarrow $ $\frac{2}{x} < 1$

$ \Rightarrow $ $2 < x$

$ \Rightarrow $ $x > 2$.

Standard 11

Mathematics

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