If the sum of the series $1 + \frac{3}{x} + \frac{9}{{{x^2}}} + \frac{{27}}{{{x^3}}} + \ldots {\rm{to\;}}\infty $ is a finite number, then

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

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Application +4 | -1

If the sum of the series

1 + \frac{3}{x} + \frac{9}{{{x^2}}} + \frac{{27}}{{{x^3}}} + \ldots \mathrm{to\;}\infty

is a finite number, then

View answer and explanation

Correct option: D

x > 3

Option D (

x > 3

) is correct because the series converges only when the absolute value of the common ratio is less than 1, which implies

|\frac{3}{x}| < 1

Practice All Chapter MCQs →

A=\{1,2,3\}, B=\{3,4\}, C=\{4,5,6\}

{A} \cup({B} \cap {C})

A-(B \cap C)

(B \cup C)-A

a,b,c

a,x,b

b,y,c

{x^2},{b^2},{y^2}

P(x)=1-x+x^2-x^3+\ldots+x^{2012}

y

Q(y)=a_0+a_1 y+\ldots+a_{2012} y^{2012}

y=x-2

\sum\limits_{{i=0}}^{2012} a_i

\log \left(\frac{5 c}{a}\right), \log \left(\frac{3 b}{5 c}\right)

\log \left(\frac{a}{3 b}\right)

A P

a, b

G P

a, b, c

\frac{3}{4}