Let $a,b,c$ be in AP. If $0 < a,\;b,c < 1,\;x = \mathop \sum \limits_{n = 0}^\infty {a^n},\;y = \mathop \sum \limits_{n = 0}^\infty {b^n}$ and $z = \mathop \sum \limits_{n = 0}^\infty {c^n}$ , then

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

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Analyzing +4 | -1

Let

a,b,c

be in AP. If

0 < a,\;b,c < 1,\;x = \sum \limits_{n = 0}^\infty {a^n},\;y = \sum \limits_{n = 0}^\infty {b^n}

and

z = \sum \limits_{n = 0}^\infty {c^n}

, then

View answer and explanation

Correct option: D

2xz = xy + yz

Option D (

2xz = xy + yz

) is correct because given that a, b, c are in AP, substituting the expressions for a, b, and c in terms of x, y, and z leads to this relationship.

Practice All Chapter MCQs →

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

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A P

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G P

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\frac{3}{4}