2011-05-09, 02:46 AM
I did that because technically, it's done in the example above me. He claimed: "The first term (1/0) should already tell you that this series is divergent".
But that's saying that
1+1^2+1^3+.... = 1/(1-1)
Which isn't something you're supposed to do since a/(1-r) is only supposed to be done when |r| <1. I make this easier to understand by showing an example (of a=1, r=2) where positive, and growing, terms somehow add up to a negative number. It's all to show that you aren't supposed to do it.
But that's saying that
1+1^2+1^3+.... = 1/(1-1)
Which isn't something you're supposed to do since a/(1-r) is only supposed to be done when |r| <1. I make this easier to understand by showing an example (of a=1, r=2) where positive, and growing, terms somehow add up to a negative number. It's all to show that you aren't supposed to do it.