Question

The value of r,such that 1+r+r2+r3...=3/5 is​

Answer 1

Answer:1/5

Step-by-step explanation:

Answer 2

Given :

$1+r+r^2+r^3+....=\dfrac{3}{5}$

To find :

The value of r i.e. $r=?$

Solution:

As we have given G.P. series,

a = 1

common ratio = $\dfrac{a_2}{a_1}=\dfrac{r}{1}=r$

So, the sum of infinite G.P. series :

$\dfrac{a}{1-r}=\dfrac{1}{1-r}=\dfrac{3}{5}\\\\5=3(1-r)\\\\5=3-3r\\\\5-3=-3r\\\\2=-3r\\\\r=\dfrac{-2}{3}$

Hence,  the value of r  is $\dfrac{-2}{3}$