${\log _e}3 - \frac{{{{\log }_e}9}}{{{2^2}}} + \frac{{{{\log }_e}27}}{{{3^2}}} - \frac{{{{\log }_e}81}}{{{4^2}}} + ...$ is

$\frac{{{{\log }_e}5}}{{{{\log }_e}3}}$

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

1 of 1

Analyzing +4 | -1

{\log _e}3 - \frac{{{{\log }_e}9}}{{{2^2}}} + \frac{{{{\log }_e}27}}{{{3^2}}} - \frac{{{{\log }_e}81}}{{{4^2}}} + ...

View answer and explanation

Correct option: A

\left( {{{\log }_e}3} \right)\left( {{{\log }_e}2} \right)

Option A (

\left( {{{\log }_e}3} \right)\left( {{{\log }_e}2} \right)

) is correct because the series can be simplified to a known logarithmic series.

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}