Question

Can someone help with a infinite geometric series question? Medal given

Answer 1

I thought i know how to do it, as i thought that the values of x where an INfinite sum occurs is when \[\left| r \right|\le1\]

Answer 2

Therefore, by logic, the values of x where there is a finite sum would be when \[\left| r \right|\ge1\]?

Answer 3

but the answer is this, so am i wrong? or is the mark scheme wrong?

Answer 4

@ganeshie8

Answer 5

\[\left| 4-3x \right|<1,-1<4-3x<1,-1-4<-3x<1-4,-5<-3x<-3\]
divide by -3
\[\frac{ -5 }{ -3 }>x>\frac{ -3 }{ -3 },\frac{ 5 }{ 3 }>x>1~or~1<x<\frac{ 5 }{ 3 }\]

Answer 6

when we multiply or divide by a negative quantity,inequality changes.