First slide

Geometric progression

Question

If $(1 - y) (1 + 2 x + 4 x^{2} + 8 x^{3} + 16 x^{4} + 32 x^{5}) = 1 - y^{6}$ , $(y \neq 1),$ then a value of $\frac{y}{x}$ is

Moderate

A

$\frac{1}{2}$
B

2
C

$\frac{1}{4}$
D

4

Solution

We can rewrite the given expression as
$(1 - y) \frac{[1 - (2 x)^{6}]}{1 - 2 x} = 1 - y^{6}$
one of the possible values of y is clearly 2x. Therefore, one of the possible values of y/x is 2.

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