Question

Find the sum of an infinitely decreasing G.P., whose first term is equal to $b+2$ and the common ratio to 2/c, where b is the least value of the product of the roots of the equation $(m^2+1)x^2-3x+(m^2+1{)}^2=0$ and c is the greatest value of the sum of its roots.

Answer 1

product of roots $=\frac{{(m^2+1)}^2}{(m^2+1)}=m^2+1$

min. $value=1$

$\Rightarrow b=1$

sum of roots = $\frac{3}{m^2+1}$

greatest value = 3

$\Rightarrow c=3$

$S_{\infty }=\frac{a}{1-8}$ = $\frac{3}{1-2/3}=9$