If $x = \mathop \sum \limits_{n = 0}^\infty {a^n},y = \mathop \sum \limits_{n = 0}^\infty {b^n},z = \mathop \sum \limits_{n = 0}^\infty {c^n},$ where $a,b,c$ are in A.P. such that $\left| a \right| < 1,\left| b \right| < 1,$ and $\left| c \right| < 1,$ then $x,y,z$ are in

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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x = \sum \limits_{n = 0}^\infty {a^n},y = \sum \limits_{n = 0}^\infty {b^n},z = \sum \limits_{n = 0}^\infty {c^n},

where

a,b,c

are in A.P. such that

\left| a \right| < 1,\left| b \right| < 1,

and

\left| c \right| < 1,

then

x,y,z

are in

View answer and explanation

Correct option: C

H.P.

Option C (H.P.) is correct because the reciprocals of x, y, and z are in A.P., implying that x, y, and z are in H.P.

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}