geometric series that converge

Hi,

For finding values of r where the geometric series converge, I've got 2 questions.

1) Do I need to 'move over' the values with r to both sides of the ineqaulity (i.e. if it's -1<3+2r<1 would I have to subtract the 3 in the middle both to the -1< side as well as the <1 side? Similarly would I then have to divide both sides by 2?

2)Even when not multiplying by -1, is there still some flipping of the inequalities sign? The reason I ask this is because I had a question where I got everything correct except for the fact that the inequalities signs where the wrong way around, but I never multiped it be -1 so I'm not sure what should have casued them to flip. This was the question: -1<3-2x<1, so I rearranged the inequality, took the values out of the middle and applied to both sides of the inequalties signs and got 2<x<1, but the answer was 2>x>1, so while I know the correct answer actually makes more sense, during the manipulation of the inequality, I did nothing to suggest I should flip the signs......


Please help!

Hi,

For finding values of r where the geometric series converge, I've got 2 questions.

1) Do I need to 'move over' the values with r to both sides of the ineqaulity (i.e. if it's -1<3+2r<1 would I have to subtract the 3 in the middle both to the -1< side as well as the <1 side? Similarly would I then have to divide both sides by 2?

2)Even when not multiplying by -1, is there still some flipping of the inequalities sign? The reason I ask this is because I had a question where I got everything correct except for the fact that the inequalities signs where the wrong way around, but I never multiped it be -1 so I'm not sure what should have casued them to flip. This was the question: -1<3-2x<1, so I rearranged the inequality, took the values out of the middle and applied to both sides of the inequalties signs and got 2<x<1, but the answer was 2>x>1, so while I know the correct answer actually makes more sense, during the manipulation of the inequality, I did nothing to suggest I should flip the signs......


Please help!

How did you go about doing that one? The most obvious way that springs to mind definitely uses division by negatives, so I'm interested to know what you did.

In general, I would say no to the question about flipping, but I would have to confirm it.

Thnaks for your reply. OK, so this is what I did for that particular question:

-1<3-2x<1
-1-3<-2x<-3+1
-4<-2x<-2
-4/-2<x<-2/-2
2<x<1 but the answer is 1<x<2

So you did divide by a negative number

Any multiplication or division of a negative number changes the inequality

Really? I thought it was only if we divided or multiplied the whole equation by a negative, like -1(1x>3-4>2x) or (1x>3-4>2x)/-1 as opposed to not flipping the sign when you're just moving things around from side to the other, in so doing reversing the operation only of what you move, like -1>x + 3 becoming -3>x+1.