Question

Y = 1+x+x^2+...... then x=​

Answer 1

Given

Y = 1+x+x^2+......

To find

The value of x

Explanation

We can clearly see that

1,x,x²,x³..................

Is a sequence

It is an infiniteG.P

$a_1=a=1\\ common \: ratio,r=\dfrac{a_2}{a_1}=\dfrac{x}{1}=x$

But

Y=sum of terms of infinite G.P

$\boxed{\bf sum \:of\: all \:terms \:in\: an \:infinite\: G.P=\dfrac{a}{1-r}}$

Substituting the values

$=>\boxed{\sf Y=\dfrac{1}{1-x}}$

Extra information

What is a G.P?

➡ Geometric progression known as G.P is a sequence in which when each term is divided by the previous term there is a common ratio r

$r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}$