JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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The sum of the infinite series

{\left( {\frac{1}{3}} \right)^2} + \frac{1}{3}{\left( {\frac{1}{3}} \right)^4} + \frac{1}{5}{\left( {\frac{1}{3}} \right)^6} + \ldots

View answer and explanation

Correct option: C

\frac{1}{6}{\log _e}2

Option C (

\frac{1}{6}{\log _e}2

) is correct because the series can be related to the logarithmic series expansion.

More Questions from SEQUENCE OF SERIES

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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

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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)

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\frac{3}{4}