Question

If y = 1 + x + x^2+ ...then x= ?
a)
$\frac{y - 1}{y}$
b)
$\frac{1 - y}{y}$
c)
$\frac{y}{1 - y}$
d) none
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Answer 1

Answer:

Option - A is the answer.

Answer 2

Solution :-

Given that,

→ y = 1 + x + x^2+ ____________ ∞ .

As , we can RHS part is GP series upto infinity , with first term as 1 and common ratio as x .

Now, we know that,

→ The sum of infinite terms of a GP series = a/(1 - r) ,

• a = First term
• r = common ratio .

Therefore,

→ y = 1 + x + x^2+ ____________ ∞

→ y = a/(1 - r)

→ y = 1/(1 - x)

→ y(1 - x) = 1

→ (1 - x) = (1/y)

→ x = 1 - (1/y)

→ x = (y - 1)/y . (option A) (Ans.)