VITEEE 2012 Paper

x = 1 + a + a2 + ... ∞ =

1

1−a

y = 1 + b + b2 + ... ∞ =

1

1−b

and z = 1 + c + c2 + ... ∞ =

1

1−c

Since, a, b and c are in AP.
⇒ 1 - a, 1 - b and 1 - c are also in AP.
⇒

1

1−a

.

1

1−b

and

1

1−c

are in HP.
∴ x, y and z are in HP.
Note that if the common ratio of a GP is not less than 1, then we do not determined the sum of an infinite GP that series