JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Medium

1 of 1

Analyzing +4 | -1

The value of

\log 2 + 2\left( {\frac{1}{5} + \frac{1}{3} \cdot \frac{1}{{{5^3}}} + \frac{1}{5} \cdot \frac{1}{{{5^5}}} + \ldots + \infty } \right)

View answer and explanation

Correct option: D

\mathrm{log\;}3

Option D (

\mathrm{log\;}3

) is correct because the expression simplifies to

\log 3

after using the logarithmic identity

\log \left( {\frac{{1 + x}}{{1 - x}}} \right) = 2\left( {x + \frac{{{x^3}}}{3} + \frac{{{x^5}}}{5} - \ldots } \right)

More Questions from SEQUENCE OF 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}