JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

1 of 1

Application +4 | -1

x = 1 + a + {a^2} + \ldots \infty

and

y = 1 + b + {b^2} + \ldots \infty

where

a

and

b

are proper fractions, then

1 + ab + {a^2}{b^2} + \ldots \infty

equals

View answer and explanation

Correct option: A

\frac{{xy}}{{y + x - 1}}

Option A (

\frac{{xy}}{{y + x - 1}}

) is correct because, given the infinite geometric series for x and y, the expression

1 + ab + {a^2}{b^2} + \ldots \infty

simplifies to

\frac{{xy}}{{x + y - 1}}

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