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If an infinite G.P. has 2nd term x and i...

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

A

`(0,2]`

B

`(1,8)`

C

`(-8,1]`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `"Sum"=((x)/(r ))/(1-r)=4` (where `r` is common ratio)
`x=4r(1-r)`
`=4(r-r^(2))`
For `r in (-1,1)`
`r-r^(2)in(-2,(1)/(4)]`
`impliesx in (-8,1]`
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