If $A=1+r^a+r^{2 a}+r^{3 a}+\ldots \ldots$ to $\infty$ and $B=1+r^b+r^{2 b}+\ldots \ldots$ to $\infty$, then $\frac{a}{b}$ is equal to

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

1 of 1

Analyzing +4 | -1

A=1+r^a+r^{2 a}+r^{3 a}+\ldots \ldots

\infty

and

B=1+r^b+r^{2 b}+\ldots \ldots

\infty

, then

\frac{a}{b}

is equal to

View answer and explanation

Correct option: B

{\log _{\left( {\frac{{B - 1}}{B}} \right)}}\left( {\frac{{A - 1}}{A}} \right)

Option B is correct because it correctly expresses the relationship between a, b, A, and B derived from the given infinite geometric series.

Practice All Chapter MCQs →

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

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(B \cup C)-A

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a,x,b

b,y,c

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

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

y

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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}