Question

If b=a+a^2+a^3 +....prove that a=b/(1+b)

Answer 1

Answer:

If b = a + a^2 + a^3 + ....., a = b / ( 1 + b ).

Step-by-step explanation:

We know,

Sum of ∞ terms of a GS is given by a / ( 1 - r ) where a is the first term and r is the common ratio of the consecutive terms.

Here, a + a^2 + a^3 + ..... forms a GS of infinite terms

First term of the GP is a.

Common ratio of the consecutive terms is a { a^2 / a or a^3 / a^2 }

On the basis of the given formula.

= > b = a / ( 1 - a )

= > b( 1 - a ) = a

= > b - ab = a

= > b = a + ab

= > b = a( 1 + b )

= > b / ( 1 + b ) = a

Henceforth, a = b / ( 1 + b ).