The value of ${\log _3}e - {\log _9}e + {\log _{27}}e - {\log _{81}}e + \ldots {\rm{ad}}.{\rm{inf}}.,$ is

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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The value of

{\log _3}e - {\log _9}e + {\log _{27}}e - {\log _{81}}e + \ldots \mathrm{ad}.\mathrm{inf}.,

View answer and explanation

Correct option: B

{\log _3}2

Option B (

{\log _3}2

) is correct because the series simplifies to a logarithmic expression using properties of logarithms and the series expansion of ln(2).

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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}