Question

If a = 1 + b + b2 + b3 + …. to ∞ , then write b in terms of a.

Answer 1

Answer:

The question, a = 1 + b + b2 + b3 + …. to ∞ is not possible to answer, because a would end up in infinity.

But if you meant, a = 1 + b + b² + b³ +.............∞ , here you go. And most importantly b must in between 1 and -1 i.e |b| ≤ 1.

$b = \frac{a-1}{a}$.

Step-by-step explanation:

a = 1 + b + b² + b³ +.............∞   ...............(1)

Multiply this expression by b,

ab = b + b² + b³................∞      ............(2)

Do (2)-(1)

ab-a = -1 + b - b + b² - b² + b³ - b³ +..................∞,

Therefore,

a(b-1) = -1,

1-b = 1/a

Therefore  $b = \frac{a-1}{a}$

Answer 2

Answer:

b= (a-1)/a

is the correct answer