Question

Question: If |r| > 1 and
x = a + a/r² + a/r⁴ + · · ·,
y = b - b/r² + b/r⁴ - · · ·,
z = c + c/r² + c/r⁴ + · · ·,
then xyz is equal to:

• A. abc
• B. acb
• C. bca
• D. 1

Hint:

Sum of infinite G.P. = (a)/(1-r) for |r|<1.

Answer 1

The Correct Option is A

Each is a G.P.:
x = a₁ - 1/r²,
y = b₁ + 1/r²,
z = c₁ - 1/r²

Thus:
(xy)/z = (ab)/c