If an infinite G.P. has 2nd term x and its sum is 4, then prove that `xin(-8,1]-{0}`

Explanation

Let the common ratio of G.P be r.
Since second term is x,first terms is x/r
Now, sum of infinite terms of G.P.=4
`rArr(x/r)/(1-r)=4`
`thereforex=4(r-r^(2))`
For `rin(-1,-1)-{0}`, we have
`r-r^(2)=1/4-(r-1/2)^(2)in(-2,1/4]-{0}`
`rArrxin(-8,1]-{0}`