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 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.

Explanation

product of roots
`=((m^2+1)^2)/(m^2+1)​=m^2+1`

min. value`(b)=1`

sum of roots = `3/(m^2+1)​`

greatest value `c=3`

` S_∞​=a/(1-8)​ = 3/(1−2/3)​=9`