JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Analyzing +4 | -1

-\pi / 2 < x < \pi / 2

, and the sum to infinite terms of the series

\cos x+\frac{2}{3} \cos x \sin ^2 x+\frac{4}{9} \cos x \sin ^4 x+\ldots

is finite then

View answer and explanation

Correct option: B

x \in(-\pi / 2, \pi / 2)

Option B (

x \in(-\pi / 2, \pi / 2)

) is correct because the sum of the infinite series converges only if the absolute value of the common ratio is less than 1, which is always true for the given range of x.

More Questions from SEQUENCE OF SERIES

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Given the sets

A=\{1,2,3\}, B=\{3,4\}, C=\{4,5,6\}

, then find the following
(i)

{A} \cup({B} \cap {C})

(ii)

A-(B \cap C)

(iii)

(B \cup C)-A

a,b,c

are in A.P.;

a,x,b

are in G.P. and

b,y,c

are in G.P., then

{x^2},{b^2},{y^2}

are in Suppose

P(x)=1-x+x^2-x^3+\ldots+x^{2012}

is expressed as a polynomial in

y

, as

Q(y)=a_0+a_1 y+\ldots+a_{2012} y^{2012}

where

y=x-2

, then

\sum\limits_{{i=0}}^{2012} a_i

equals If

\log \left(\frac{5 c}{a}\right), \log \left(\frac{3 b}{5 c}\right)

and

\log \left(\frac{a}{3 b}\right)

are in

A P

, where

a, b

and c are in

G P

, then

a, b, c

are the lengths of sides of If the sum of three numbers in G.P. is 63 and the product of the first and the second term is

\frac{3}{4}

of the third term, then the numbers are If the lengths of sides of a right angled triangle are in A.P., then their ratio is