Sum of first $n$ terms in the series ${\cot ^{ - 1}}3 + {\cot ^{ - 1}}7 + {\rm{co}}{{\rm{t}}^{ - 1}}13 + {\cot ^{ - 1}}21 + \ldots $ is given by

${\tan ^{ - 1}}\left( {\frac{n}{{n + 2}}} \right)$

${\cot ^{ - 1}}\left( {\frac{{n + 2}}{n}} \right)$

${\tan ^{ - 1}}\left( {n + 1} \right) - {\tan ^{ - 1}}1$

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

1 of 1

Analyzing +4 | -1

Sum of first

n

terms in the series

{\cot ^{ - 1}}3 + {\cot ^{ - 1}}7 + \mathrm{co}{\mathrm{t}^{ - 1}}13 + {\cot ^{ - 1}}21 + \ldots

is given by

View answer and explanation

Correct option: D

All of these

Option D (All of these) is correct because the sum of the series can be expressed in multiple equivalent forms using trigonometric identities.

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}